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50
The BNS Lower Bound for MultiParty Protocols is Nearly Optimal
 Information and Computation
, 1994
"... We present a multiparty protocol which computes the Generalized Inner Product (GIP) function, introduced by Babai, Nisan and Szegedy [BNS]. Our protocol shows that the lower bound for the multiparty communication complexity of the GIP function, given by [BNS], cannot be improved significantly. ..."
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We present a multiparty protocol which computes the Generalized Inner Product (GIP) function, introduced by Babai, Nisan and Szegedy [BNS]. Our protocol shows that the lower bound for the multiparty communication complexity of the GIP function, given by [BNS], cannot be improved significantly. keywords: multiparty communication, communication protocols 1. INTRODUCTION In the twoparty communication game, introduced by Yao [Y], there are two players, P 0 and P 1 , and a function f : f0; 1g 2n ! f0; 1g. The goal of the players is to compute the value of f(A 0 ; A 1 ) cooperatively, for some A 0 ; A 1 2 f0; 1g n , where A 0 is known only to P 1 , and A 1 is known only to P 0 , and after the computation both players should know the value f(A 0 ; A 1 ). The players have unlimited computational power, and both know the definition of f . P 0 and P 1 communicate via a blackboard, which is seen by both of them: they are allowed to write bits on the blackboard. The cost of the compu...
The rank and size of graphs
 J. of Graph Theory
, 1996
"... We show that the number of points with pairwise different sets of neighbors in a graph is O(2 r/2) where r is the rank of the adjacency matrix. We also give an example that achieves this bound. 1 ..."
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We show that the number of points with pairwise different sets of neighbors in a graph is O(2 r/2) where r is the rank of the adjacency matrix. We also give an example that achieves this bound. 1
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 13 (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...
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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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.
A strong direct product theorem for disjointness
 In 42nd ACM Symposium on Theory of Computing (STOC
, 2010
"... A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then the overall success probability will be exponentially small in k. We establish such a theorem for the randomized communication co ..."
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A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then the overall success probability will be exponentially small in k. We establish such a theorem for the randomized communication complexity of the Disjointness problem, i.e., with communication const · kn the success probability of solving k instances can only be exponentially small in k. We show that this bound even holds in an AM communication protocol with limited ambiguity. The main result implies a new lower bound for Disjointness in a restricted 3player NOF protocol, and optimal communicationspace tradeoffs for Boolean matrix product. Our main result follows from a solution to the dual of a linear programming problem, whose feasibility comes from a socalled Intersection Sampling Lemma that generalizes a result by Razborov [Raz92]. We also discuss a new lower bound technique for randomized communication complexity called the generalized rectangle bound that we use in our proof. 1
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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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...
Lower Bounds for Fundamental Geometric Problems
 IN 5TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA'97
, 1996
"... We develop lower bounds on the number of primitive operations required to solve several fundamental problems in computational geometry. For example, given a set of points in the plane, are any three colinear? Given a set of points and lines, does any point lie on a line? These and similar question ..."
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We develop lower bounds on the number of primitive operations required to solve several fundamental problems in computational geometry. For example, given a set of points in the plane, are any three colinear? Given a set of points and lines, does any point lie on a line? These and similar questions arise as subproblems or special cases of a large number of more complicated geometric problems, including point location, range searching, motion planning, collision detection, ray shooting, and hidden surface removal. Previously these problems were studied only in general models of computation, but known techniques for these models are too weak to prove useful results. Our approach is to consider, for each problem, a more specialized model of computation that is still rich enough to describe all known algorit...
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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While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem
Upper and Lower Bounds for Certain GraphAccessibilityProblems on Bounded Alternating ωBranching Programs
 MFCS'91, LNCS 520
, 1991
"... In the following we investigate the computational complexity of various ωGRAPH ACCESSIBILITY PROBLEMs on the most general restricted type of !branching programs for which, up to now, exponential lower bounds on the size can be proved. By means of exponential lower bounds on various ranks of certai ..."
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In the following we investigate the computational complexity of various ωGRAPH ACCESSIBILITY PROBLEMs on the most general restricted type of !branching programs for which, up to now, exponential lower bounds on the size can be proved. By means of exponential lower bounds on various ranks of certain communication matrices we prove that ωGRAPH ACCESSIBILITY PROBLEMs can not be computed by bounded alternating ωbranching programs within polynomial size. In contrast, ωGRAPH ACCESSIBILITY PROBLEMs restricted to monotone graphs can by computed by such devices.