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60
Complexity of Graph Partition Problems
 31ST ANNUAL ACM STOC
, 1999
"... We introduce a parametrized family of graph problems that includes several wellknown graph partition problems as special cases. We develop tools which allow us to classify the complexity of many problems in this family, and in particular lead us to a complete classification for small values of the ..."
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Cited by 21 (4 self)
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We introduce a parametrized family of graph problems that includes several wellknown graph partition problems as special cases. We develop tools which allow us to classify the complexity of many problems in this family, and in particular lead us to a complete classification for small values of the parameters. Along the way, we obtain a variety of specific results including the following: a generalization of a communication bound on the number of cliqueversusindependentset separators; polynomialtime algorithms to recognize generalized split graphs; and, a quasipolynomial algorithm for the Skew Cutset Problem that essentially resolves an open problem posed by Chv'atal. The last two problems have interesting connections to the Strong Perfect Graph Conjecture of Berge.
On Frege and Extended Frege Proof Systems
, 1993
"... We propose a framework for proving lower bounds to the size of EF  proofs (equivalently, to the number of proofsteps in Fproofs) in terms of boolean valuations . The concept is motivated by properties of propositional provability in models of bounded arithmetic and it is a finitisation of a parti ..."
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Cited by 21 (4 self)
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We propose a framework for proving lower bounds to the size of EF  proofs (equivalently, to the number of proofsteps in Fproofs) in terms of boolean valuations . The concept is motivated by properties of propositional provability in models of bounded arithmetic and it is a finitisation of a particular forcing construction explained also in the paper. It reduces the question of proving a lower bound to the question of constructing a partial boolean algebra and a map of formulas into that algebra with particular properties. We show that in principle one can obtain via this method optimal lower bounds (up to a polynomial increase). Introduction A propositional proof system is any polynomial time function P whose range is exactly the set of tautologies TAUT, cf. [17]. For ø a tautology any string ß such that P (ß) = ø is called a P proof of ø . Any usual propositional calculus, be it resolution or extended resolution, a Hilbert style system based on finitely many axiom schemes and inf...
Communication Complexity in a 3Computer Model
, 1996
"... It is proved that the probabilistic communication complexity of the identity function in a 3computer model is O(√n). ..."
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Cited by 20 (1 self)
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It is proved that the probabilistic communication complexity of the identity function in a 3computer model is O(√n).
Scaling bounds for function computation over large networks
 in Information Theory, IEEE Intl. Symposium on
, 2007
"... Abstract — We develop order bounds on the refresh rate of computing two classes of functions over large multihop sensor networks – namely, typethreshold (e.g. max) and typesensitive functions (e.g. average). The refresh rate quantifies how often the function can be recomputed with new data at se ..."
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Cited by 18 (2 self)
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Abstract — We develop order bounds on the refresh rate of computing two classes of functions over large multihop sensor networks – namely, typethreshold (e.g. max) and typesensitive functions (e.g. average). The refresh rate quantifies how often the function can be recomputed with new data at sensor nodes. We first show that for typethreshold functions optimal refresh rate of Θ(1) is possible over networks whose connectivity graphs have finite degree. Next, even for a simple representative typesensitive function, we show that the maximum refresh rate that can be achieved in a wide class of networks of n nodes with any multihop digital communication scheme is at most Θ(1 / log n), if the goal is to compute the function with deterministic guarantees. On the other hand, we show that relaxing the requirements to allow probabilistic guarantees enables a refresh rate of Θ(1) over any graph with bounded degree and a refresh rate of Θ(1/log log n) for random planar networks. Further, for such networks operating over an AWGN channel with signal power pathloss, we show that even refresh rate of Θ(1) can be achieved with vanishing distortion when the power pathloss exponent is strictly less than 4. Thus, relaxing deterministic computation guarantees to probabilistic requirements enables sizeable improvement in refresh rates. I.
The partition bound for classical communication complexity and query complexity
 In Proceedings of the 25th Conference on Computational Complexity (CCC
, 2010
"... We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the partition bound is stronger than both the rectangle/corruption boun ..."
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Cited by 16 (4 self)
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We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the partition bound is stronger than both the rectangle/corruption bound and the γ2/generalized discrepancy bounds. In the model of query complexity we show that the partition bound is stronger than the approximate polynomial degree and classical adversary bounds. We also exhibit an example where the partition bound is quadratically larger than the approximate polynomial degree and adversary bounds.
Lower Bounds for NonCommutative Computation (Extended Abstract)
 Proceedings of the 23rd ACM Symposium on Theory of Computing, ACM Press
, 1991
"... We consider algebraic computations which are not allowed to rely on the commutativity of multiplication. We obtain various lower bounds for algebraic formula size in this model: (1) Computing the determinant is as hard as computing the permanent and tight exponential upper and lower bounds are given ..."
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Cited by 15 (0 self)
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We consider algebraic computations which are not allowed to rely on the commutativity of multiplication. We obtain various lower bounds for algebraic formula size in this model: (1) Computing the determinant is as hard as computing the permanent and tight exponential upper and lower bounds are given. (2) Computation cannot be parallelized, as opposed to in the commutative case  this solves in the negative an open problem of Miller et al [8]. (3) The question of the power of negation in this model is shown to be closely related to a well known open problem relating communication complexity and rank.
Competitive Paging And DualGuided OnLine Weighted Caching And Matching Algorithms
, 1991
"... This thesis presents research done by the author on competitive analysis of online problems. An online problem is a problem that is given and solved one piece at a time. An online strategy for solving such a problem must give the solution to each piece knowing only the current piece and preceding ..."
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Cited by 12 (0 self)
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This thesis presents research done by the author on competitive analysis of online problems. An online problem is a problem that is given and solved one piece at a time. An online strategy for solving such a problem must give the solution to each piece knowing only the current piece and preceding pieces, in ignorance of the pieces to be given in the future. We consider online strategies that are competitive (guaranteeing solutions whose costs are within a constant factor of optimal) for several combinatorial optimization problems: paging, weighted caching, the kserver problem, and weighted matching. We introduce variations on the standard model of competitive analysis for paging: allowing randomization, allowing resourcebounded lookahead, and loose competitiveness, in which performance over a range of fast memory sizes is considered and noncompetitiveness is allowed provided the fault rate is insignificant. Each variation leads to substantially better competitive ratios. We prese...
Randomized Simultaneous Messages
 Proc. 12th IEEE Symp. on Computational Complexity
, 1996
"... In the twoplayer communication model introduced by Yao [Y79], Alice and Bob wish to collaboratively evaluate a function f(x; y) in which Alice knows only input x and Bob knows only input y. Both players have unlimited computational power. The objective is to minimize the amount of communication. Y ..."
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Cited by 9 (0 self)
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In the twoplayer communication model introduced by Yao [Y79], Alice and Bob wish to collaboratively evaluate a function f(x; y) in which Alice knows only input x and Bob knows only input y. Both players have unlimited computational power. The objective is to minimize the amount of communication. Yao [Y79] also introduced an oblivious version of this communication game which we call the simultaneous messages (SM) model. The difference is that in the SM model, Alice and Bob don't communicate with each other. Instead, they simultaneously send a message to a referee, who sees none of the inputs. The referee then announces the function value. The deterministic twoplayer SM complexity of any function is straightforward to determine. Yao suggested the randomized version of this model, where each player has access to private coin flips. Our main result is that the order of magnitude of the randomized SM complexity of any function f is at least the square root of the deterministic SM compl...
Communication Complexity Method for Measuring Nondeterminism in Finite Automata
, 2000
"... While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem ..."
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Cited by 9 (1 self)
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While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem