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Mark Braverman - One of the best experts on this subject based on the ideXlab platform.
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near optimal bounds on the bounded round quantum communication complexity of Disjointness
SIAM Journal on Computing, 2018Co-Authors: Mark Braverman, Ankit Garg, Jieming Mao, Dave TouchetteAbstract:We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of Disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r...
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a rounds vs communication tradeoff for multi party set Disjointness
Foundations of Computer Science, 2017Co-Authors: Mark Braverman, Rotem OshmanAbstract:In the set disjointess problem, we have k players, each with a private input X^i ⊆ [n], and the goal is for the players to determine whether or not their sets have a global intersection. The players communicate over a shared blackboard, and we charge them for each bit that they write on the board.We study the trade-off between the number of interaction rounds we allow the players, and the total number of bits they must send to solve set Disjointness. We show that if R rounds of interaction are allowed, the communication cost is Ω(nk^{1/R}/R^4), which is nearly tight. We also leverage our proof to show that wellfare maximization with unit demand bidders cannot be solved efficiently in a small number of rounds: here, we have k players bidding on n items, and the goal is to find a matching between items and player that bid on them which approximately maximizes the total number of items assigned. It was previously shown by Alon et. al. that Ω(log log k) rounds of interaction are required to find an assignment which achieves a constant approximation to the maximum-wellfare assignment, even if each player is allowed to write n^{≥(R)} bits on the board in each round, where ≥(R) = exp(-R). We improve this lower bound to Ωlog k / log log k), which is known to be tight up to a log log k factor.
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near optimal bounds on bounded round quantum communication complexity of Disjointness
Foundations of Computer Science, 2015Co-Authors: Mark Braverman, Ankit Garg, Jieming Mao, Dave TouchetteAbstract:We prove a near optimal round-communication trade off for the two-party quantum communication complexity of Disjointness. For protocols with r rounds, we prove a lower bound of a#x03A9;(n/r) on the communication required for computing Disjointness of input size n, which is optimal up to logarithmic factors. The previous best lower bound was a#x03A9;(n/r2) due to Jain, Radha krishnan and Sen. Along the way, we develop several tools for quantum information complexity, one of which is a lower bound for quantum information complexity in terms of the generalized discrepancy method. As a corollary, we get that the quantum communication complexity of any boolean function f is at most 2O(QIC(f)), where QIC(f) is the prior-free quantum information complexity of f (with error 1/3).
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near optimal bounds on bounded round quantum communication complexity of Disjointness
arXiv: Computational Complexity, 2015Co-Authors: Mark Braverman, Ankit Garg, Jieming Mao, Dave TouchetteAbstract:We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of Disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r + r)$ on the communication required for computing Disjointness of input size $n$, which is optimal up to logarithmic factors. The previous best lower bound was $\Omega(n/r^2 + r)$ due to Jain, Radhakrishnan and Sen [JRS03]. Along the way, we develop several tools for quantum information complexity, one of which is a lower bound for quantum information complexity in terms of the generalized discrepancy method. As a corollary, we get that the quantum communication complexity of any boolean function $f$ is at most $2^{O(QIC(f))}$, where $QIC(f)$ is the prior-free quantum information complexity of $f$ (with error $1/3$).
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a tight bound for set Disjointness in the message passing model
Foundations of Computer Science, 2013Co-Authors: Mark Braverman, Toniann Pitassi, Rotem Oshman, Faith Ellen, Vinod VaikuntanathanAbstract:In a multiparty message-passing model of communication, there are k players. Each player has a private input, and they communicate by sending messages to one another over private channels. While this model has been used extensively in distributed computing and in secure multiparty computation, lower bounds on communication complexity in this model and related models have been somewhat scarce. In recent work [25], [29], [30], strong lower bounds of the form Ω(n·k) were obtained for several functions in the message-passing model; however, a lower bound on the classical set Disjointness problem remained elusive. In this paper, we prove a tight lower bound of Ω(n · k) for the set Disjointness problem in the message passing model. Our bound is obtained by developing information complexity tools for the message-passing model and proving an information complexity lower bound for set Disjointness.
Dave Touchette - One of the best experts on this subject based on the ideXlab platform.
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near optimal bounds on the bounded round quantum communication complexity of Disjointness
SIAM Journal on Computing, 2018Co-Authors: Mark Braverman, Ankit Garg, Jieming Mao, Dave TouchetteAbstract:We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of Disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r...
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near optimal bounds on bounded round quantum communication complexity of Disjointness
Foundations of Computer Science, 2015Co-Authors: Mark Braverman, Ankit Garg, Jieming Mao, Dave TouchetteAbstract:We prove a near optimal round-communication trade off for the two-party quantum communication complexity of Disjointness. For protocols with r rounds, we prove a lower bound of a#x03A9;(n/r) on the communication required for computing Disjointness of input size n, which is optimal up to logarithmic factors. The previous best lower bound was a#x03A9;(n/r2) due to Jain, Radha krishnan and Sen. Along the way, we develop several tools for quantum information complexity, one of which is a lower bound for quantum information complexity in terms of the generalized discrepancy method. As a corollary, we get that the quantum communication complexity of any boolean function f is at most 2O(QIC(f)), where QIC(f) is the prior-free quantum information complexity of f (with error 1/3).
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near optimal bounds on bounded round quantum communication complexity of Disjointness
arXiv: Computational Complexity, 2015Co-Authors: Mark Braverman, Ankit Garg, Jieming Mao, Dave TouchetteAbstract:We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of Disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r + r)$ on the communication required for computing Disjointness of input size $n$, which is optimal up to logarithmic factors. The previous best lower bound was $\Omega(n/r^2 + r)$ due to Jain, Radhakrishnan and Sen [JRS03]. Along the way, we develop several tools for quantum information complexity, one of which is a lower bound for quantum information complexity in terms of the generalized discrepancy method. As a corollary, we get that the quantum communication complexity of any boolean function $f$ is at most $2^{O(QIC(f))}$, where $QIC(f)$ is the prior-free quantum information complexity of $f$ (with error $1/3$).
Nathan Segerlind - One of the best experts on this subject based on the ideXlab platform.
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lower bounds for lovasz schrijver systems and beyond follow from multiparty communication complexity
SIAM Journal on Computing, 2007Co-Authors: Paul Beame, Toniann Pitassi, Nathan SegerlindAbstract:We prove that an $\omega(\log^4 n)$ lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-Disjointness function implies an $n^{\omega(1)}$ size lower bound for treelike Lovasz-Schrijver systems that refute unsatisfiable formulas in conjunctive normal form (CNFs). More generally, we prove that an $n^{\Omega(1)}$ lower bound for the $(k+1)$-party NOF communication complexity of set Disjointness implies a $2^{n^{\Omega(1)}}$ size lower bound for all treelike proof systems whose formulas are degree $k$ polynomial inequalities.
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a strong direct product theorem for corruption and the multiparty communication complexity of Disjointness
Computational Complexity, 2006Co-Authors: Paul Beame, Toniann Pitassi, Nathan Segerlind, Avi WigdersonAbstract:We prove that two-party randomized communication complexity satisfies a strong direct product property, so long as the communication lower bound is proved by a "corruption" or "one-sided discrepancy" method over a rectangular distribution. We use this to prove new n ?(1) lower bounds for 3-player number-on-the-forehead protocols in which the first player speaks once and then the other two players proceed arbitrarily. Using other techniques, we also establish an ?(n 1/(k?1)/(k ? 1)) lower bound for k-player randomized number-on-the-forehead protocols for the Disjointness function in which all messages are broadcast simultaneously. A simple corollary of this is that general randomized number-on-the-forehead protocols require ?(log n/(k ? 1)) bits of communication to compute the Disjointness function.
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lower bounds for lovasz schrijver systems and beyond follow from multiparty communication complexity
International Colloquium on Automata Languages and Programming, 2005Co-Authors: Paul Beame, Toniann Pitassi, Nathan SegerlindAbstract:We prove that an ω(log3n) lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-Disjointness function implies an nω(1) size lower bound for tree-like Lovasz-Schrijver systems that refute unsatisfiable CNFs. More generally, we prove that an nΩ(1) lower bound for the (k+1)-party NOF communication complexity of set-Disjointness implies a $2^{n^{\Omega(1)}}$ size lower bound for all tree-like proof systems whose formulas are degree k polynomial inequalities.
Toniann Pitassi - One of the best experts on this subject based on the ideXlab platform.
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a tight bound for set Disjointness in the message passing model
Foundations of Computer Science, 2013Co-Authors: Mark Braverman, Toniann Pitassi, Rotem Oshman, Faith Ellen, Vinod VaikuntanathanAbstract:In a multiparty message-passing model of communication, there are k players. Each player has a private input, and they communicate by sending messages to one another over private channels. While this model has been used extensively in distributed computing and in secure multiparty computation, lower bounds on communication complexity in this model and related models have been somewhat scarce. In recent work [25], [29], [30], strong lower bounds of the form Ω(n·k) were obtained for several functions in the message-passing model; however, a lower bound on the classical set Disjointness problem remained elusive. In this paper, we prove a tight lower bound of Ω(n · k) for the set Disjointness problem in the message passing model. Our bound is obtained by developing information complexity tools for the message-passing model and proving an information complexity lower bound for set Disjointness.
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lower bounds for lovasz schrijver systems and beyond follow from multiparty communication complexity
SIAM Journal on Computing, 2007Co-Authors: Paul Beame, Toniann Pitassi, Nathan SegerlindAbstract:We prove that an $\omega(\log^4 n)$ lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-Disjointness function implies an $n^{\omega(1)}$ size lower bound for treelike Lovasz-Schrijver systems that refute unsatisfiable formulas in conjunctive normal form (CNFs). More generally, we prove that an $n^{\Omega(1)}$ lower bound for the $(k+1)$-party NOF communication complexity of set Disjointness implies a $2^{n^{\Omega(1)}}$ size lower bound for all treelike proof systems whose formulas are degree $k$ polynomial inequalities.
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a strong direct product theorem for corruption and the multiparty communication complexity of Disjointness
Computational Complexity, 2006Co-Authors: Paul Beame, Toniann Pitassi, Nathan Segerlind, Avi WigdersonAbstract:We prove that two-party randomized communication complexity satisfies a strong direct product property, so long as the communication lower bound is proved by a "corruption" or "one-sided discrepancy" method over a rectangular distribution. We use this to prove new n ?(1) lower bounds for 3-player number-on-the-forehead protocols in which the first player speaks once and then the other two players proceed arbitrarily. Using other techniques, we also establish an ?(n 1/(k?1)/(k ? 1)) lower bound for k-player randomized number-on-the-forehead protocols for the Disjointness function in which all messages are broadcast simultaneously. A simple corollary of this is that general randomized number-on-the-forehead protocols require ?(log n/(k ? 1)) bits of communication to compute the Disjointness function.
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lower bounds for lovasz schrijver systems and beyond follow from multiparty communication complexity
International Colloquium on Automata Languages and Programming, 2005Co-Authors: Paul Beame, Toniann Pitassi, Nathan SegerlindAbstract:We prove that an ω(log3n) lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-Disjointness function implies an nω(1) size lower bound for tree-like Lovasz-Schrijver systems that refute unsatisfiable CNFs. More generally, we prove that an nΩ(1) lower bound for the (k+1)-party NOF communication complexity of set-Disjointness implies a $2^{n^{\Omega(1)}}$ size lower bound for all tree-like proof systems whose formulas are degree k polynomial inequalities.
Paul Beame - One of the best experts on this subject based on the ideXlab platform.
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lower bounds for lovasz schrijver systems and beyond follow from multiparty communication complexity
SIAM Journal on Computing, 2007Co-Authors: Paul Beame, Toniann Pitassi, Nathan SegerlindAbstract:We prove that an $\omega(\log^4 n)$ lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-Disjointness function implies an $n^{\omega(1)}$ size lower bound for treelike Lovasz-Schrijver systems that refute unsatisfiable formulas in conjunctive normal form (CNFs). More generally, we prove that an $n^{\Omega(1)}$ lower bound for the $(k+1)$-party NOF communication complexity of set Disjointness implies a $2^{n^{\Omega(1)}}$ size lower bound for all treelike proof systems whose formulas are degree $k$ polynomial inequalities.
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a strong direct product theorem for corruption and the multiparty communication complexity of Disjointness
Computational Complexity, 2006Co-Authors: Paul Beame, Toniann Pitassi, Nathan Segerlind, Avi WigdersonAbstract:We prove that two-party randomized communication complexity satisfies a strong direct product property, so long as the communication lower bound is proved by a "corruption" or "one-sided discrepancy" method over a rectangular distribution. We use this to prove new n ?(1) lower bounds for 3-player number-on-the-forehead protocols in which the first player speaks once and then the other two players proceed arbitrarily. Using other techniques, we also establish an ?(n 1/(k?1)/(k ? 1)) lower bound for k-player randomized number-on-the-forehead protocols for the Disjointness function in which all messages are broadcast simultaneously. A simple corollary of this is that general randomized number-on-the-forehead protocols require ?(log n/(k ? 1)) bits of communication to compute the Disjointness function.
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lower bounds for lovasz schrijver systems and beyond follow from multiparty communication complexity
International Colloquium on Automata Languages and Programming, 2005Co-Authors: Paul Beame, Toniann Pitassi, Nathan SegerlindAbstract:We prove that an ω(log3n) lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-Disjointness function implies an nω(1) size lower bound for tree-like Lovasz-Schrijver systems that refute unsatisfiable CNFs. More generally, we prove that an nΩ(1) lower bound for the (k+1)-party NOF communication complexity of set-Disjointness implies a $2^{n^{\Omega(1)}}$ size lower bound for all tree-like proof systems whose formulas are degree k polynomial inequalities.
