The Experts below are selected from a list of 404433 Experts worldwide ranked by ideXlab platform
Kasper Green Larsen - One of the best experts on this subject based on the ideXlab platform.
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tight cell probe bounds for succinct boolean matrix vector multiplication
Symposium on the Theory of Computing, 2018Co-Authors: Diptarka Chakraborty, Lior Kamma, Kasper Green LarsenAbstract:The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous Important Data Structure problems, see Henzinger et al. [STOC’15]. In recent work, Larsen and Williams [SODA’17] attacked the problem from the upper bound side and gave a surprising cell probe Data Structure (that is, we only charge for memory accesses, while computation is free). Their cell probe Data Structure answers queries in O(n7/4) time and is succinct in the sense that it stores the input matrix in read-only memory, plus an additional O(n7/4) bits on the side. In this paper, we essentially settle the cell probe complexity of succinct Boolean matrix-vector multiplication. We present a new cell probe Data Structure with query time O(n3/2) storing just O(n3/2) bits on the side. We then complement our Data Structure with a lower bound showing that any Data Structure storing r bits on the side, with n
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tight cell probe bounds for succinct boolean matrix vector multiplication
arXiv: Data Structures and Algorithms, 2017Co-Authors: Diptarka Chakraborty, Lior Kamma, Kasper Green LarsenAbstract:The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous Important Data Structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and Williams [SODA'17] attacked the problem from the upper bound side and gave a surprising cell probe Data Structure (that is, we only charge for memory accesses, while computation is free). Their cell probe Data Structure answers queries in $\tilde{O}(n^{7/4})$ time and is succinct in the sense that it stores the input matrix in read-only memory, plus an additional $\tilde{O}(n^{7/4})$ bits on the side. In this paper, we essentially settle the cell probe complexity of succinct Boolean matrix-vector multiplication. We present a new cell probe Data Structure with query time $\tilde{O}(n^{3/2})$ storing just $\tilde{O}(n^{3/2})$ bits on the side. We then complement our Data Structure with a lower bound showing that any Data Structure storing $r$ bits on the side, with $n < r < n^2$ must have query time $t$ satisfying $t r = \tilde{\Omega}(n^3)$. For $r \leq n$, any Data Structure must have $t = \tilde{\Omega}(n^2)$. Since lower bounds in the cell probe model also apply to classic word-RAM Data Structures, the lower bounds naturally carry over. We also prove similar lower bounds for matrix-vector multiplication over $\mathbb{F}_2$.
Diptarka Chakraborty - One of the best experts on this subject based on the ideXlab platform.
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tight cell probe bounds for succinct boolean matrix vector multiplication
Symposium on the Theory of Computing, 2018Co-Authors: Diptarka Chakraborty, Lior Kamma, Kasper Green LarsenAbstract:The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous Important Data Structure problems, see Henzinger et al. [STOC’15]. In recent work, Larsen and Williams [SODA’17] attacked the problem from the upper bound side and gave a surprising cell probe Data Structure (that is, we only charge for memory accesses, while computation is free). Their cell probe Data Structure answers queries in O(n7/4) time and is succinct in the sense that it stores the input matrix in read-only memory, plus an additional O(n7/4) bits on the side. In this paper, we essentially settle the cell probe complexity of succinct Boolean matrix-vector multiplication. We present a new cell probe Data Structure with query time O(n3/2) storing just O(n3/2) bits on the side. We then complement our Data Structure with a lower bound showing that any Data Structure storing r bits on the side, with n
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tight cell probe bounds for succinct boolean matrix vector multiplication
arXiv: Data Structures and Algorithms, 2017Co-Authors: Diptarka Chakraborty, Lior Kamma, Kasper Green LarsenAbstract:The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous Important Data Structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and Williams [SODA'17] attacked the problem from the upper bound side and gave a surprising cell probe Data Structure (that is, we only charge for memory accesses, while computation is free). Their cell probe Data Structure answers queries in $\tilde{O}(n^{7/4})$ time and is succinct in the sense that it stores the input matrix in read-only memory, plus an additional $\tilde{O}(n^{7/4})$ bits on the side. In this paper, we essentially settle the cell probe complexity of succinct Boolean matrix-vector multiplication. We present a new cell probe Data Structure with query time $\tilde{O}(n^{3/2})$ storing just $\tilde{O}(n^{3/2})$ bits on the side. We then complement our Data Structure with a lower bound showing that any Data Structure storing $r$ bits on the side, with $n < r < n^2$ must have query time $t$ satisfying $t r = \tilde{\Omega}(n^3)$. For $r \leq n$, any Data Structure must have $t = \tilde{\Omega}(n^2)$. Since lower bounds in the cell probe model also apply to classic word-RAM Data Structures, the lower bounds naturally carry over. We also prove similar lower bounds for matrix-vector multiplication over $\mathbb{F}_2$.
Lior Kamma - One of the best experts on this subject based on the ideXlab platform.
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tight cell probe bounds for succinct boolean matrix vector multiplication
Symposium on the Theory of Computing, 2018Co-Authors: Diptarka Chakraborty, Lior Kamma, Kasper Green LarsenAbstract:The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous Important Data Structure problems, see Henzinger et al. [STOC’15]. In recent work, Larsen and Williams [SODA’17] attacked the problem from the upper bound side and gave a surprising cell probe Data Structure (that is, we only charge for memory accesses, while computation is free). Their cell probe Data Structure answers queries in O(n7/4) time and is succinct in the sense that it stores the input matrix in read-only memory, plus an additional O(n7/4) bits on the side. In this paper, we essentially settle the cell probe complexity of succinct Boolean matrix-vector multiplication. We present a new cell probe Data Structure with query time O(n3/2) storing just O(n3/2) bits on the side. We then complement our Data Structure with a lower bound showing that any Data Structure storing r bits on the side, with n
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tight cell probe bounds for succinct boolean matrix vector multiplication
arXiv: Data Structures and Algorithms, 2017Co-Authors: Diptarka Chakraborty, Lior Kamma, Kasper Green LarsenAbstract:The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous Important Data Structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and Williams [SODA'17] attacked the problem from the upper bound side and gave a surprising cell probe Data Structure (that is, we only charge for memory accesses, while computation is free). Their cell probe Data Structure answers queries in $\tilde{O}(n^{7/4})$ time and is succinct in the sense that it stores the input matrix in read-only memory, plus an additional $\tilde{O}(n^{7/4})$ bits on the side. In this paper, we essentially settle the cell probe complexity of succinct Boolean matrix-vector multiplication. We present a new cell probe Data Structure with query time $\tilde{O}(n^{3/2})$ storing just $\tilde{O}(n^{3/2})$ bits on the side. We then complement our Data Structure with a lower bound showing that any Data Structure storing $r$ bits on the side, with $n < r < n^2$ must have query time $t$ satisfying $t r = \tilde{\Omega}(n^3)$. For $r \leq n$, any Data Structure must have $t = \tilde{\Omega}(n^2)$. Since lower bounds in the cell probe model also apply to classic word-RAM Data Structures, the lower bounds naturally carry over. We also prove similar lower bounds for matrix-vector multiplication over $\mathbb{F}_2$.
Katherine Yelick - One of the best experts on this subject based on the ideXlab platform.
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a local view array library for partitioned global address space c programs
Programming Language Design and Implementation, 2014Co-Authors: Amir Kamil, Yili Zheng, Katherine YelickAbstract:Multidimensional arrays are an Important Data Structure in many scientific applications. Unfortunately, built-in support for such arrays is inadequate in C++, particularly in the distributed setting where bulk communication operations are required for good performance. In this paper, we present a multidimensional library for partitioned global address space (PGAS) programs, supporting the one-sided remote access and bulk operations of the PGAS model. The library is based on Titanium arrays, which have proven to provide good productivity and performance. These arrays provide a local view of Data, where each rank constructs its own portion of a global Data Structure, matching the local view of execution common to PGAS programs and providing maximum flexibility in structuring global Data. Unlike Titanium, which has its own compiler with array-specific analyses, optimizations, and code generation, we implement multidimensional arrays solely through a C++ library. The main goal of this effort is to provide a library-based implementation that can match the productivity and performance of a compiler-based approach. We implement the array library as an extension to UPC++, a C++ library for PGAS programs, and we extend Titanium arrays with specializations to improve performance. We evaluate the array library by porting four Titanium benchmarks to UPC++, demonstrating that it can achieve up to 25% better performance than Titanium without a significant increase in programmer effort.
Amir Kamil - One of the best experts on this subject based on the ideXlab platform.
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a local view array library for partitioned global address space c programs
Programming Language Design and Implementation, 2014Co-Authors: Amir Kamil, Yili Zheng, Katherine YelickAbstract:Multidimensional arrays are an Important Data Structure in many scientific applications. Unfortunately, built-in support for such arrays is inadequate in C++, particularly in the distributed setting where bulk communication operations are required for good performance. In this paper, we present a multidimensional library for partitioned global address space (PGAS) programs, supporting the one-sided remote access and bulk operations of the PGAS model. The library is based on Titanium arrays, which have proven to provide good productivity and performance. These arrays provide a local view of Data, where each rank constructs its own portion of a global Data Structure, matching the local view of execution common to PGAS programs and providing maximum flexibility in structuring global Data. Unlike Titanium, which has its own compiler with array-specific analyses, optimizations, and code generation, we implement multidimensional arrays solely through a C++ library. The main goal of this effort is to provide a library-based implementation that can match the productivity and performance of a compiler-based approach. We implement the array library as an extension to UPC++, a C++ library for PGAS programs, and we extend Titanium arrays with specializations to improve performance. We evaluate the array library by porting four Titanium benchmarks to UPC++, demonstrating that it can achieve up to 25% better performance than Titanium without a significant increase in programmer effort.
