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25
Matching is as Easy as Matrix Inversion
, 1987
"... A new algorithm for finding a maximum matching in a general graph is presented; its special feature being that the only computationally nontrivial step required in its execution is the inversion of a single integer matrix. Since this step can be parallelized, we get a simple parallel (RNC2) algorit ..."
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Cited by 166 (5 self)
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A new algorithm for finding a maximum matching in a general graph is presented; its special feature being that the only computationally nontrivial step required in its execution is the inversion of a single integer matrix. Since this step can be parallelized, we get a simple parallel (RNC2) algorithm. At the heart of our algorithm lies a probabilistic lemma, the isolating lemma. We show applications of this lemma to parallel computation and randomized reductions.
On the approximability of tradeoffs and optimal access of web sources (Extended Abstract)
 Proceedings 41st Annual Symposium on Foundations of Computer Science
, 2000
"... We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the tradeoff between these objectives (the socalled Pareto curve). We point out that, under very general condit ..."
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Cited by 107 (2 self)
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We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the tradeoff between these objectives (the socalled Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that approximates the Pareto curve, for any > 0. We give a necessary and sucient condition under which this approximate Pareto curve can be constructed in time polynomial in the size of the instance and 1=. In the case of multiple linear objectives, we distinguish between two cases: When the underlying feasible region is convex, then we show that approximating the multiobjective problem is equivalent to approximating the singleobjective problem. If, however, the feasible region is discrete, then we point out that the question reduces to an old and recurrent one: How does the complexity of a combinatorial optimization problem change when its feasible region is intresected with a hyperplane with small coefficients; we report some interesting new ndings in this domain. Finally, we apply these concepts and techniques to formulate and solve approximately a costtimequality tradeoff for optimizing access to the worldwide web, in a model first studied by Etzioni et al [EHJ+] (which was actually the original motivation for this work).
On the Security of MultiParty PingPong Protocols
, 1985
"... This paper is concerned with the model for security of cryptographic protocols suggested by Dolev and Yao. The Dolev and Yao model deals with a restricted class of protocols, known as TwoParty PingPong Protocols. In such a protocol, messages are exchanged in a memoryless manner. That is, the mess ..."
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Cited by 59 (1 self)
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This paper is concerned with the model for security of cryptographic protocols suggested by Dolev and Yao. The Dolev and Yao model deals with a restricted class of protocols, known as TwoParty PingPong Protocols. In such a protocol, messages are exchanged in a memoryless manner. That is, the message sent by each party results from applying a predetermined operator to the message he has received. The Dolev and Yao model is presented, generalized in various directions and the affect of these generalizations is extensively studied. First, the model is trivially generalized to deal with multiparty pingpong protocols. However, the problems which arise from this generalization are very far from being trivial. In particular, it is no longer clear how many saboteurs (adversaries) should be considered when testing the security of pparty pingpong protocols. We demonstrate an upper bound of 3(p \Gamma 2) + 2 and a lower bound of 3(p \Gamma 2) + 1 on this number. Thus, for every fixed p, th...
Winner determination in sequential majority voting
 In Proceedings of the ECAI2006 Multidisciplinary Workshop on Advances in Preference Handling
, 2007
"... Preferences can be aggregated using a voting rule. Each agent gives their preference orderings over a set of candidates, and a voting rule is used to compute the winner. We consider voting rules which perform a sequence of pairwise comparisons between two candidates, where the result of each is comp ..."
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Cited by 38 (12 self)
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Preferences can be aggregated using a voting rule. Each agent gives their preference orderings over a set of candidates, and a voting rule is used to compute the winner. We consider voting rules which perform a sequence of pairwise comparisons between two candidates, where the result of each is computed by a majority vote. The winner thus depends on the chosen sequence of comparisons, which can be represented by a binary tree. There are candidates that will win in some trees (called possible winners) or in all trees (called Condorcet winners). While it is easy to find the possible and Condorcet winners, we prove that it is difficult if we insist that the tree is balanced. This restriction is therefore enough to make voting difficult for the chair to manipulate. We also consider the situation where we lack complete informations about preferences, and determine the computational complexity of computing possible and Condorcet winners in this extended case. 1
Computational methods for the diameter restricted minimum weight spanning tree problem
 Australasian Journal of Combinatorics
, 1994
"... Let G be a simple undirected graph with nonnegative edge weights. In this paper we consider the following combinatorial optimization problem: Find, in G, a minimum weight spanning tree having diameter at most D. This problem is trivial for D:S 3 and NPcomplete for D:: 4. In this paper we develop a ..."
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Cited by 14 (0 self)
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Let G be a simple undirected graph with nonnegative edge weights. In this paper we consider the following combinatorial optimization problem: Find, in G, a minimum weight spanning tree having diameter at most D. This problem is trivial for D:S 3 and NPcomplete for D:: 4. In this paper we develop and implement a number of Branch and Bound algorithms for this problem. Computational results, based on simulated problems, are discussed. 1.
R.: Nfold integer programming
 Disc. Optim
"... Abstract. Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. Th ..."
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Cited by 13 (5 self)
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Abstract. Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations
Fixing a tournament
 In Proceedings of AAAI’10
, 2010
"... We consider a very natural problem concerned with game manipulation. Let G be a directed graph where the nodes represent players of a game, and an edge from u to v means that u can beat v in the game. (If an edge (u, v) is not present, one cannot match u and v.) Given G and a “favorite ” node A, is ..."
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Cited by 12 (5 self)
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We consider a very natural problem concerned with game manipulation. Let G be a directed graph where the nodes represent players of a game, and an edge from u to v means that u can beat v in the game. (If an edge (u, v) is not present, one cannot match u and v.) Given G and a “favorite ” node A, is it possible to set up the bracket of a balanced singleelimination tournament so that A is guaranteed to win, if matches occur as predicted by G? We show that the problem is NPcomplete for general graphs. For the case when G is a tournament graph we give several interesting conditions on the desired winner A for which there exists a balanced singleelimination tournament which A wins, and it can be found in polynomial time.
Decision making based on approximate and smoothed pareto curves
 In Proc. of 16th ISAAC
, 2005
"... We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the socalled decision maker’s approach in which both criteria are combined into a single (usually nonlinear) objective function. Pr ..."
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Cited by 11 (2 self)
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We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the socalled decision maker’s approach in which both criteria are combined into a single (usually nonlinear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curve for problems like Shortest Path, Spanning Tree, and Perfect Matching. We wish to determine for which classes of combined objective functions the approximate Pareto curve also yields an approximate solution to the decision maker’s problem. We show that an FPTAS for the Pareto curve also gives an FPTAS for the decision maker’s problem if the combined objective function is growth bounded like a quasipolynomial function. If the objective function, however, shows exponential growth then the decision maker’s problem is NPhard to approximate within any polynomial factor. In order to bypass these limitations of approximate decision making, we turn our attention to Pareto curves in the probabilistic framework of smoothed analysis. We show that in a smoothed model, we can efficiently generate the (complete and exact) Pareto curve with a small failure probability if there exists an algorithm for generating the Pareto curve whose worst case running time is pseudopolynomial. This way, we can solve the decision maker’s problem w.r.t. any nondecreasing objective function for randomly perturbed instances of, e. g.,
Budgeted matching and budgeted matroid intersection via the gasoline puzzle
 In proc. IPCO 2008
"... Abstract. Many polynomialtime solvable combinatorial optimization problems become NPhard if an additional complicating constraint is added to restrict the set of feasible solutions. In this paper, we consider two such problems, namely maximumweight matching and maximumweight matroid intersection ..."
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Cited by 9 (1 self)
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Abstract. Many polynomialtime solvable combinatorial optimization problems become NPhard if an additional complicating constraint is added to restrict the set of feasible solutions. In this paper, we consider two such problems, namely maximumweight matching and maximumweight matroid intersection with one additional budget constraint. We present the first polynomialtime approximation schemes for these problems. Similarly to other approaches for related problems, our schemes compute two solutions to the Lagrangian relaxation of the problem and patch them together to obtain a nearoptimal solution. However, due to the richer combinatorial structure of the problems considered here, standard patching techniques do not apply. To circumvent this problem, we crucially exploit the adjacency relations on the solution polytope and, surprisingly, the solution to an old combinatorial puzzle. 1
Approximation algorithms for multicriteria traveling salesman problems
, 2006
"... In multicriteria optimization, several objective functions are to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as optimal. Instead, the aim is to compute socalled Pareto curves. Since Pareto curves c ..."
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Cited by 7 (4 self)
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In multicriteria optimization, several objective functions are to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as optimal. Instead, the aim is to compute socalled Pareto curves. Since Pareto curves cannot be computed efficiently in general, we have to be content with approximations to them. We are concerned with approximating Pareto curves of multicriteria traveling salesman problems (TSP). We provide algorithms for computing approximate Pareto curves for the symmetric TSP with triangle inequality ( ∆STSP), symmetric and asymmetric TSP with strengthened triangle inequality (∆(γ)STSP and ∆(γ)ATSP), and symmetric and asymmetric TSP with weights one and two (STSP(1, 2) and ATSP(1, 2)). We design a deterministic polynomialtime algorithm that computes (1 + γ + ε)approximate Pareto curves for multicriteria ∆(γ)STSP for γ ∈ [ 1, 1]. We also present two randomized approximation algo2 rithms for multicriteria ∆(γ)STSP achieving approximation ratios of