The Experts below are selected from a list of 219 Experts worldwide ranked by ideXlab platform
Muriel Médard - One of the best experts on this subject based on the ideXlab platform.
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On Network Functional Compression
IEEE Transactions on Information Theory, 2014Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this thesis, we consider different aspects of the functional compression problem. In functional compression, the computation of a function (or, some functions) of sources is desired at the receiver(s). The rate region of this problem has been considered in the literature under certain restrictive assumptions. In Chapter 2 of this Thesis, we consider this problem for an arbitrary tree network and asymptotically lossless computations. In particular, for one-stage tree networks, we compute a rate-region and for an arbitrary tree network, we derive a rate lower bound based on the Graph entropy. We introduce a new condition on colorings of source random variables' Characteristic Graphs called the coloring connectivity condition (C.C.C.). We show that unlike the condition mentioned in Doshi et al., this condition is necessary and sufficient for any achievable coding scheme based on colorings. We also show that, unlike entropy, Graph entropy does not satisfy the chain rule. For one stage trees with correlated sources, and general trees with independent sources, we propose a modularized coding scheme based on Graph colorings to perform arbitrarily closely to the derived rate lower bound. We show that in a general tree network case with independent sources, to achieve the rate lower bound, intermediate nodes should perform some computations. However, for a family of functions and random variables called chain rule proper sets, it is sufficient to have intermediate nodes act like relays to perform arbitrarily closely to the rate lower bound. In Chapter 3 of this Thesis, we consider a multi-functional version of this problem with side information, where the receiver wants to compute several functions with different side information random variables and zero distortion. Our results are applicable to the case with several receivers computing different desired functions. We define a new concept named multi-functional Graph entropy which is an extension of Graph entropy defined by K6rner. We show that the minimum achievable rate for this problem is equal to conditional multi-functional Graph entropy of the source random variable given the side information. We also propose a coding scheme based on Graph colorings to achieve this rate. In these proposed coding schemes, one needs to compute the minimum entropy coloring (a coloring random variable which minimizes the entropy) of a Characteristic Graph. In general, finding this coloring is an NP-hard problem. However, in Chapter 4, we show that depending on the Characteristic Graph's structure, there are some interesting cases where finding the minimum entropy coloring is not NP-hard, but tractable and practical. In one of these cases, we show that, by having a non-zero joint probability condition on random variables' distributions, for any desired function, finding the minimum entropy coloring can be solved in polynomial time. In another case, we show that if the desired function is a quantization function, this problem is also tractable. We also consider this problem in a general…
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On Network Functional Compression
IEEE Transactions on Information Theory, 2014Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this paper, we consider different aspects of the problem of compressing for function computation across a network, which we call network functional compression. In network functional compression, computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of this problem has been considered in the literature under certain restrictive assumptions, particularly in terms of the network topology, the functions, and the Characteristics of the sources. In this paper, we present results that significantly relax these assumptions. For a one-stage tree network, we characterize a rate region by introducing a necessary and sufficient condition for any achievable coloring-based coding scheme called coloring connectivity condition. We also propose a modularized coding scheme based on Graph colorings to perform arbitrarily closely to rate lower bounds. For a general tree network, we provide a rate lower bound based on Graph entropies and show that, this bound is tight in the case of having independent sources. In particular, we show that, in a general tree network case with independent sources, to achieve the rate lower bound, intermediate nodes should perform computations. However, for a family of functions and random variables, which we call chain-rule proper sets, it is sufficient to have no computations at intermediate nodes to perform arbitrarily closely to the rate lower bound. In addition, we consider practical issues of coloring-based coding schemes and propose an efficient algorithm to compute a minimum entropy coloring of a Characteristic Graph under some conditions on source distributions and/or the desired function. Finally, extensions of these results for cases of having feedback and lossy function computations are discussed.
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Cases where finding the minimum entropy coloring of a Characteristic Graph is a polynomial time problem
2010 IEEE International Symposium on Information Theory, 2010Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this paper, we consider the problem of finding the minimum entropy coloring of a Characteristic Graph under some conditions which allow it to be in polynomial time. This problem arises in the functional compression problem where the computation of a function of sources is desired at the receiver. The rate region of the functional compression problem has been considered in some references under some assumptions. Recently, Feizi et al. computed this rate region for a general one-stage tree network and its extension to a general tree network. In their proposed coding scheme, one needs to compute the minimum entropy coloring (a coloring random variable which minimizes the entropy) of a Characteristic Graph. In general, finding this coloring is an NP-hard problem (as shown by Cardinal et al.). However, in this paper, we show that depending on the Characteristic Graph's structure, there are some interesting cases where finding the minimum entropy coloring is not NP-hard, but tractable and practical. In one of these cases, we show that, having a non-zero joint probability condition on RVs' distributions, for any desired function f, makes Characteristic Graphs to be formed of some non-overlapping fully-connected maximal independent sets. Therefore, the minimum entropy coloring can be solved in polynomial time. In another case, we show that if f is a quantization function, this problem is also tractable.
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ISIT - Cases where finding the minimum entropy coloring of a Characteristic Graph is a polynomial time problem
2010 IEEE International Symposium on Information Theory, 2010Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this paper, we consider the problem of finding the minimum entropy coloring of a Characteristic Graph under some conditions which allow it to be in polynomial time. This problem arises in the functional compression problem where the computation of a function of sources is desired at the receiver. The rate region of the functional compression problem has been considered in some references under some assumptions. Recently, Feizi et al. computed this rate region for a general one-stage tree network and its extension to a general tree network. In their proposed coding scheme, one needs to compute the minimum entropy coloring (a coloring random variable which minimizes the entropy) of a Characteristic Graph. In general, finding this coloring is an NP-hard problem (as shown by Cardinal et al.). However, in this paper, we show that depending on the Characteristic Graph's structure, there are some interesting cases where finding the minimum entropy coloring is not NP-hard, but tractable and practical. In one of these cases, we show that, having a non-zero joint probability condition on RVs' distributions, for any desired function f, makes Characteristic Graphs to be formed of some non-overlapping fully-connected maximal independent sets. Therefore, the minimum entropy coloring can be solved in polynomial time. In another case, we show that if f is a quantization function, this problem is also tractable.
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GLOBECOM - Multi-Functional Compression with Side Information
GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference, 2009Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this paper, we consider the problem of multifunctional compression with side information. The problem is how we can compress a source X so that the receiver is able to compute some deterministic functions f1(X, Y1), ..., fm(X, Ym), where Yi, 1 ≤ i ≤ m, are available at the receiver as side information. In [1], Wyner and Ziv considered this problem for the special case of m = 1 and f1(X, Y1) = X and derived a rate-distortion function. Yamamoto extended this result in [2] to the case of having one general function f1(X, Y1). Both of these results were in terms of an auxiliary random variable. For the case of zero distortion, in [3], Orlitsky and Roche gave an interpretation of this variable in terms of properties of the Characteristic Graph which led to a particular coding scheme. This result was extended in [4] by providing an achievable scheme based on colorings of the Characteristic Graph. In a recent work, reference [5] has considered this problem for a general tree network where intermediate nodes are allowed to perform some computations. These previous works only considered the case where the receiver only wants to compute one function (m=1). Here, we want to consider the case in which the receiver wants to compute several functions with different side information random variables and zero distortion. Our results do not depend on the fact that all functions are desired in one receiver and one can apply them to the case of having several receivers with different desired functions (i.e., functions are separable). We define a new concept named the multi-functional Graph entropy which is an extension of the Graph entropy defined by Korner in [6]. We show that the minimum achievable rate for this problem is equal to the conditional multi-functional Graph entropy of random variable X given side informations. We also propose a coding scheme based on Graph colorings to achieve this rate.
Tomoyuki Uchida - One of the best experts on this subject based on the ideXlab platform.
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acquisition of Characteristic sets of block preserving outerplanar Graph patterns by a two stage evolutionary learning method for Graph pattern sets
International Journal of Computational Intelligence Studies, 2018Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:Knowledge acquisition from Graph structured data is an important task in machine learning and data mining. Block preserving outerplanar Graph patterns are Graph structured patterns having structured variables and are suited to represent Characteristic Graph structures of Graph data modelled as outerplanar Graphs. We propose a learning method for acquiring Characteristic sets of block preserving outerplanar Graph patterns by a two-stage evolutionary learning method for Graph pattern sets as individuals, from positive and negative outerplanar Graph data, in order to represent Characteristic Graph structures more concretely.
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Aggregative context-aware fitness functions based on feature selection for evolutionary learning of Characteristic Graph patterns
Vietnam Journal of Computer Science, 2018Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose aggregative context-aware fitness functions based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness functions estimate the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specify the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness functions to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic block-preserving outerplanar Graph patterns and Characteristic TTSP Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness functions.
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IWCIA - Acquisition of multiple block preserving outerplanar Graph patterns by an evolutionary method for Graph pattern sets
2017 IEEE 10th International Workshop on Computational Intelligence and Applications (IWCIA), 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:Knowledge acquisition from Graph structured data is an important task in machine learning and data mining. Block preserving outerplanar Graph patterns are Graph structured patterns having structured variables and are suited to represent Characteristic Graph structures of Graph data modeled as outerplanar Graphs. We propose a learning method for acquiring Characteristic multiple block preserving outerplanar Graph patterns by evolutionary computation using Graph pattern sets as individuals, from positive and negative outerplanar Graph data, in order to represent Characteristic Graph structures more precisely.
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a context aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns
Asian Conference on Intelligent Information and Database Systems, 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose a context-aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness function estimates the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specifies the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness function to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness function and a previous fitness function ignoring context.
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ACIIDS (1) - A Context-Aware Fitness Function Based on Feature Selection for Evolutionary Learning of Characteristic Graph Patterns
Intelligent Information and Database Systems, 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose a context-aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness function estimates the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specifies the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness function to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness function and a previous fitness function ignoring context.
Fumiya Tokuhara - One of the best experts on this subject based on the ideXlab platform.
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acquisition of Characteristic sets of block preserving outerplanar Graph patterns by a two stage evolutionary learning method for Graph pattern sets
International Journal of Computational Intelligence Studies, 2018Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:Knowledge acquisition from Graph structured data is an important task in machine learning and data mining. Block preserving outerplanar Graph patterns are Graph structured patterns having structured variables and are suited to represent Characteristic Graph structures of Graph data modelled as outerplanar Graphs. We propose a learning method for acquiring Characteristic sets of block preserving outerplanar Graph patterns by a two-stage evolutionary learning method for Graph pattern sets as individuals, from positive and negative outerplanar Graph data, in order to represent Characteristic Graph structures more concretely.
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Aggregative context-aware fitness functions based on feature selection for evolutionary learning of Characteristic Graph patterns
Vietnam Journal of Computer Science, 2018Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose aggregative context-aware fitness functions based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness functions estimate the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specify the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness functions to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic block-preserving outerplanar Graph patterns and Characteristic TTSP Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness functions.
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IWCIA - Acquisition of multiple block preserving outerplanar Graph patterns by an evolutionary method for Graph pattern sets
2017 IEEE 10th International Workshop on Computational Intelligence and Applications (IWCIA), 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:Knowledge acquisition from Graph structured data is an important task in machine learning and data mining. Block preserving outerplanar Graph patterns are Graph structured patterns having structured variables and are suited to represent Characteristic Graph structures of Graph data modeled as outerplanar Graphs. We propose a learning method for acquiring Characteristic multiple block preserving outerplanar Graph patterns by evolutionary computation using Graph pattern sets as individuals, from positive and negative outerplanar Graph data, in order to represent Characteristic Graph structures more precisely.
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a context aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns
Asian Conference on Intelligent Information and Database Systems, 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose a context-aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness function estimates the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specifies the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness function to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness function and a previous fitness function ignoring context.
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ACIIDS (1) - A Context-Aware Fitness Function Based on Feature Selection for Evolutionary Learning of Characteristic Graph Patterns
Intelligent Information and Database Systems, 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose a context-aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness function estimates the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specifies the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness function to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness function and a previous fitness function ignoring context.
Tetsuji Kuboyama - One of the best experts on this subject based on the ideXlab platform.
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acquisition of Characteristic sets of block preserving outerplanar Graph patterns by a two stage evolutionary learning method for Graph pattern sets
International Journal of Computational Intelligence Studies, 2018Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:Knowledge acquisition from Graph structured data is an important task in machine learning and data mining. Block preserving outerplanar Graph patterns are Graph structured patterns having structured variables and are suited to represent Characteristic Graph structures of Graph data modelled as outerplanar Graphs. We propose a learning method for acquiring Characteristic sets of block preserving outerplanar Graph patterns by a two-stage evolutionary learning method for Graph pattern sets as individuals, from positive and negative outerplanar Graph data, in order to represent Characteristic Graph structures more concretely.
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Aggregative context-aware fitness functions based on feature selection for evolutionary learning of Characteristic Graph patterns
Vietnam Journal of Computer Science, 2018Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose aggregative context-aware fitness functions based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness functions estimate the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specify the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness functions to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic block-preserving outerplanar Graph patterns and Characteristic TTSP Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness functions.
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IWCIA - Acquisition of multiple block preserving outerplanar Graph patterns by an evolutionary method for Graph pattern sets
2017 IEEE 10th International Workshop on Computational Intelligence and Applications (IWCIA), 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:Knowledge acquisition from Graph structured data is an important task in machine learning and data mining. Block preserving outerplanar Graph patterns are Graph structured patterns having structured variables and are suited to represent Characteristic Graph structures of Graph data modeled as outerplanar Graphs. We propose a learning method for acquiring Characteristic multiple block preserving outerplanar Graph patterns by evolutionary computation using Graph pattern sets as individuals, from positive and negative outerplanar Graph data, in order to represent Characteristic Graph structures more precisely.
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a context aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns
Asian Conference on Intelligent Information and Database Systems, 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose a context-aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness function estimates the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specifies the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness function to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness function and a previous fitness function ignoring context.
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ACIIDS (1) - A Context-Aware Fitness Function Based on Feature Selection for Evolutionary Learning of Characteristic Graph Patterns
Intelligent Information and Database Systems, 2017Co-Authors: Fumiya Tokuhara, Tetsuhiro Miyahara, Tetsuji Kuboyama, Yusuke Suzuki, Tomoyuki UchidaAbstract:We propose a context-aware fitness function based on feature selection for evolutionary learning of Characteristic Graph patterns. The proposed fitness function estimates the fitness of a set of correlated individuals rather than the sum of fitness of the individuals, and specifies the fitness of an individual as its contribution degree in the context of the set. We apply the proposed fitness function to our evolutionary learning, based on Genetic Programming, for obtaining Characteristic Graph patterns from positive and negative Graph data. We report some experimental results on our evolutionary learning of Characteristic Graph patterns, using the context-aware fitness function and a previous fitness function ignoring context.
Soheil Feizi - One of the best experts on this subject based on the ideXlab platform.
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On Network Functional Compression
IEEE Transactions on Information Theory, 2014Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this thesis, we consider different aspects of the functional compression problem. In functional compression, the computation of a function (or, some functions) of sources is desired at the receiver(s). The rate region of this problem has been considered in the literature under certain restrictive assumptions. In Chapter 2 of this Thesis, we consider this problem for an arbitrary tree network and asymptotically lossless computations. In particular, for one-stage tree networks, we compute a rate-region and for an arbitrary tree network, we derive a rate lower bound based on the Graph entropy. We introduce a new condition on colorings of source random variables' Characteristic Graphs called the coloring connectivity condition (C.C.C.). We show that unlike the condition mentioned in Doshi et al., this condition is necessary and sufficient for any achievable coding scheme based on colorings. We also show that, unlike entropy, Graph entropy does not satisfy the chain rule. For one stage trees with correlated sources, and general trees with independent sources, we propose a modularized coding scheme based on Graph colorings to perform arbitrarily closely to the derived rate lower bound. We show that in a general tree network case with independent sources, to achieve the rate lower bound, intermediate nodes should perform some computations. However, for a family of functions and random variables called chain rule proper sets, it is sufficient to have intermediate nodes act like relays to perform arbitrarily closely to the rate lower bound. In Chapter 3 of this Thesis, we consider a multi-functional version of this problem with side information, where the receiver wants to compute several functions with different side information random variables and zero distortion. Our results are applicable to the case with several receivers computing different desired functions. We define a new concept named multi-functional Graph entropy which is an extension of Graph entropy defined by K6rner. We show that the minimum achievable rate for this problem is equal to conditional multi-functional Graph entropy of the source random variable given the side information. We also propose a coding scheme based on Graph colorings to achieve this rate. In these proposed coding schemes, one needs to compute the minimum entropy coloring (a coloring random variable which minimizes the entropy) of a Characteristic Graph. In general, finding this coloring is an NP-hard problem. However, in Chapter 4, we show that depending on the Characteristic Graph's structure, there are some interesting cases where finding the minimum entropy coloring is not NP-hard, but tractable and practical. In one of these cases, we show that, by having a non-zero joint probability condition on random variables' distributions, for any desired function, finding the minimum entropy coloring can be solved in polynomial time. In another case, we show that if the desired function is a quantization function, this problem is also tractable. We also consider this problem in a general…
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On Network Functional Compression
IEEE Transactions on Information Theory, 2014Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this paper, we consider different aspects of the problem of compressing for function computation across a network, which we call network functional compression. In network functional compression, computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of this problem has been considered in the literature under certain restrictive assumptions, particularly in terms of the network topology, the functions, and the Characteristics of the sources. In this paper, we present results that significantly relax these assumptions. For a one-stage tree network, we characterize a rate region by introducing a necessary and sufficient condition for any achievable coloring-based coding scheme called coloring connectivity condition. We also propose a modularized coding scheme based on Graph colorings to perform arbitrarily closely to rate lower bounds. For a general tree network, we provide a rate lower bound based on Graph entropies and show that, this bound is tight in the case of having independent sources. In particular, we show that, in a general tree network case with independent sources, to achieve the rate lower bound, intermediate nodes should perform computations. However, for a family of functions and random variables, which we call chain-rule proper sets, it is sufficient to have no computations at intermediate nodes to perform arbitrarily closely to the rate lower bound. In addition, we consider practical issues of coloring-based coding schemes and propose an efficient algorithm to compute a minimum entropy coloring of a Characteristic Graph under some conditions on source distributions and/or the desired function. Finally, extensions of these results for cases of having feedback and lossy function computations are discussed.
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Cases where finding the minimum entropy coloring of a Characteristic Graph is a polynomial time problem
2010 IEEE International Symposium on Information Theory, 2010Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this paper, we consider the problem of finding the minimum entropy coloring of a Characteristic Graph under some conditions which allow it to be in polynomial time. This problem arises in the functional compression problem where the computation of a function of sources is desired at the receiver. The rate region of the functional compression problem has been considered in some references under some assumptions. Recently, Feizi et al. computed this rate region for a general one-stage tree network and its extension to a general tree network. In their proposed coding scheme, one needs to compute the minimum entropy coloring (a coloring random variable which minimizes the entropy) of a Characteristic Graph. In general, finding this coloring is an NP-hard problem (as shown by Cardinal et al.). However, in this paper, we show that depending on the Characteristic Graph's structure, there are some interesting cases where finding the minimum entropy coloring is not NP-hard, but tractable and practical. In one of these cases, we show that, having a non-zero joint probability condition on RVs' distributions, for any desired function f, makes Characteristic Graphs to be formed of some non-overlapping fully-connected maximal independent sets. Therefore, the minimum entropy coloring can be solved in polynomial time. In another case, we show that if f is a quantization function, this problem is also tractable.
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ISIT - Cases where finding the minimum entropy coloring of a Characteristic Graph is a polynomial time problem
2010 IEEE International Symposium on Information Theory, 2010Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this paper, we consider the problem of finding the minimum entropy coloring of a Characteristic Graph under some conditions which allow it to be in polynomial time. This problem arises in the functional compression problem where the computation of a function of sources is desired at the receiver. The rate region of the functional compression problem has been considered in some references under some assumptions. Recently, Feizi et al. computed this rate region for a general one-stage tree network and its extension to a general tree network. In their proposed coding scheme, one needs to compute the minimum entropy coloring (a coloring random variable which minimizes the entropy) of a Characteristic Graph. In general, finding this coloring is an NP-hard problem (as shown by Cardinal et al.). However, in this paper, we show that depending on the Characteristic Graph's structure, there are some interesting cases where finding the minimum entropy coloring is not NP-hard, but tractable and practical. In one of these cases, we show that, having a non-zero joint probability condition on RVs' distributions, for any desired function f, makes Characteristic Graphs to be formed of some non-overlapping fully-connected maximal independent sets. Therefore, the minimum entropy coloring can be solved in polynomial time. In another case, we show that if f is a quantization function, this problem is also tractable.
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GLOBECOM - Multi-Functional Compression with Side Information
GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference, 2009Co-Authors: Soheil Feizi, Muriel MédardAbstract:In this paper, we consider the problem of multifunctional compression with side information. The problem is how we can compress a source X so that the receiver is able to compute some deterministic functions f1(X, Y1), ..., fm(X, Ym), where Yi, 1 ≤ i ≤ m, are available at the receiver as side information. In [1], Wyner and Ziv considered this problem for the special case of m = 1 and f1(X, Y1) = X and derived a rate-distortion function. Yamamoto extended this result in [2] to the case of having one general function f1(X, Y1). Both of these results were in terms of an auxiliary random variable. For the case of zero distortion, in [3], Orlitsky and Roche gave an interpretation of this variable in terms of properties of the Characteristic Graph which led to a particular coding scheme. This result was extended in [4] by providing an achievable scheme based on colorings of the Characteristic Graph. In a recent work, reference [5] has considered this problem for a general tree network where intermediate nodes are allowed to perform some computations. These previous works only considered the case where the receiver only wants to compute one function (m=1). Here, we want to consider the case in which the receiver wants to compute several functions with different side information random variables and zero distortion. Our results do not depend on the fact that all functions are desired in one receiver and one can apply them to the case of having several receivers with different desired functions (i.e., functions are separable). We define a new concept named the multi-functional Graph entropy which is an extension of the Graph entropy defined by Korner in [6]. We show that the minimum achievable rate for this problem is equal to the conditional multi-functional Graph entropy of random variable X given side informations. We also propose a coding scheme based on Graph colorings to achieve this rate.