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Approximation techniques for utilitarian mechanism design
 IN PROC. 36TH ACM SYMP. ON THEORY OF COMPUTING
, 2005
"... This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multiparameter agents. We focus on approximation algorithms for NPhard mechanism design problems. These algorithms need to satisfy certain monotonic ..."
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Cited by 64 (3 self)
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This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multiparameter agents. We focus on approximation algorithms for NPhard mechanism design problems. These algorithms need to satisfy certain monotonicity properties to ensure truthfulness. Since most of the known approximation techniques do not fulfill these properties, we study alternative techniques. Our first contribution is a quite general method to transform a pseudopolynomial algorithm into a monotone FPTAS. This can be applied to various problems like, e.g., knapsack, constrained shortest path, or job scheduling with deadlines. For example, the monotone FPTAS for the knapsack problem gives a very efficient, truthful mechanism for singleminded multiunit auctions. The best previous result for such auctions was a 2approximation. In addition,
A constantfactor approximation algorithm for packet routing, and balancing local vs. global criteria
 In Proceedings of the ACM Symposium on the Theory of Computing (STOC
, 1997
"... Abstract. We present the first constantfactor approximation algorithm for a fundamental problem: the storeandforward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, this algorithmbalances a global criterio ..."
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Cited by 46 (5 self)
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Abstract. We present the first constantfactor approximation algorithm for a fundamental problem: the storeandforward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, this algorithmbalances a global criterion (routing time) with a local criterion (maximum queue size) and shows how to get simultaneous good bounds for both. For this particular problem, approximating the routing time well, even without considering the queue sizes, was open. We then consider a class of such local vs. global problems in the context of covering integer programs and show how to improve the local criterion by a logarithmic factor by losing a constant factor in the global criterion.
Algorithmic construction of sets for krestrictions
 ACM TRANSACTIONS ON ALGORITHMS
, 2006
"... This work addresses krestriction problems, which unify combinatorial problems of the following type: The goal is to construct a short list of strings in Σ m that satisfies a given set of kwise demands. For every k positions and every demand, there must be at least one string in the list that satis ..."
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Cited by 44 (2 self)
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This work addresses krestriction problems, which unify combinatorial problems of the following type: The goal is to construct a short list of strings in Σ m that satisfies a given set of kwise demands. For every k positions and every demand, there must be at least one string in the list that satisfies the demand at these positions. Problems of this form frequently arise in different fields in Computer Science. The standard approach for deterministically solving such problems is via almost kwise independence or kwise approximations for other distributions. We offer a generic algorithmic method that yields considerably smaller constructions. To this end, we generalize a previous work of Naor, Schulman and Srinivasan [18]. Among other results, we greatly enhance the combinatorial objects in the heart of their method, called splitters, and construct multiway splitters, using a new discrete version of the topological Necklace Splitting Theorem [1]. We utilize our methods to show improved constructions for group testing [19] and generalized hashing [3], and an improved inapproximability result for SetCover under the assumption P != NP.
Approximation Algorithms for the Unsplittable Flow Problem
"... We present approximation algorithms for the unsplittable flow problem (UFP) on undirected graphs. As is standard in this line of research, we assume that the maximum demand is at most the minimum capacity. We focus on the nonuniform capacity case in which the edge capacities can vary arbitrarily ..."
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Cited by 42 (7 self)
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We present approximation algorithms for the unsplittable flow problem (UFP) on undirected graphs. As is standard in this line of research, we assume that the maximum demand is at most the minimum capacity. We focus on the nonuniform capacity case in which the edge capacities can vary arbitrarily over the graph. Our results are: For undirected graphs we obtain a O(\Delta ff \Gamma 1 log2 n) approximation ratio, where n is the number of vertices, \Delta the maximum degree, and ff the expansion of the graph. Our ratio is capacity independent and improves upon the earlier O(\Delta ff \Gamma 1(c max=cmin) log n) bound [15] for large values of cmax=cmin. Furthermore, if we specialize to the case where all edges have the same capacity, our algorithm gives an O(\Delta ff \Gamma 1 log n) approximation, which matches the performance of the bestknown algorithm [15] for this special case. For certain strong constantdegree expanders considered by Frieze [10] we obtain an O(plog n) approximation for the uniform capacity case, improving upon the current O(log n) approximation. For UFP on the line and the ring, we give the first constantfactor approximation algorithms. Previous results addressed only the uniform capacity case. All of the above results improve if the maximum demand is bounded
An Extension of the Lovász Local Lemma, and its Applications to Integer Programming
 In Proceedings of the 7th Annual ACMSIAM Symposium on Discrete Algorithms
, 1996
"... The Lov'asz Local Lemma (LLL) is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events, each of which asserts that a random variable does not deviate much from its mea ..."
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Cited by 31 (6 self)
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The Lov'asz Local Lemma (LLL) is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events, each of which asserts that a random variable does not deviate much from its mean. We consider three classes of NPhard integer programs: minimax, packing, and covering integer programs. A key technique, randomized rounding of linear relaxations, was developed by Raghavan & Thompson to derive good approximation algorithms for such problems. We use our extended LLL to prove that randomized rounding produces, with nonzero probability, much better feasible solutions than known before, if the constraint matrices of these integer programs are sparse (e.g., VLSI routing using short paths, problems on hypergraphs with small dimension/degree). We also generalize the method of pessimistic estimators due to Raghavan, to constructivize our packing and covering results. 1
Tight Approximation Results for General Covering Integer Programs
 In Proc. of the FortySecond Annual Symposium on Foundations of Computer Science
, 2001
"... In this paper we study approximation algorithms for solving a general covering integer program. An nvector x of nonnegative integers is sought, which minimizes c T x; subject to Ax b; x d: The entries of A; b; c are nonnegative. Let m be the number of rows of A: Covering problems have been hea ..."
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Cited by 20 (3 self)
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In this paper we study approximation algorithms for solving a general covering integer program. An nvector x of nonnegative integers is sought, which minimizes c T x; subject to Ax b; x d: The entries of A; b; c are nonnegative. Let m be the number of rows of A: Covering problems have been heavily studied in combinatorial optimization. We focus on the effect of the multiplicity constraints, x d; on approximability. Two longstanding open questions remain for this general formulation with upper bounds on the variables. (i) The integrality gap of the standard LP relaxation is arbitrarily large. Existing approximation algorithms that achieve the wellknown O(log m)approximation with respect to the LP value do so at the expense of violating the upper bounds on the variables by the same O(log m) multiplicative factor. What is the smallest possible violation of the upper bounds that still achieves cost within O(log m) of the standard LP optimum ? (ii) The best known approximation ratio for the problem has been O(log(max j P i A ij )) since 1982. This bound can be as bad as polynomial in the input size. Is an O(log m)approximation, like the one known for the special case of Set Cover, possible? We settle these two open questions. To answer the first question we give an algorithm based on the relatively simple new idea of randomly rounding variables to smallerthaninteger units. To settle the second question we give a reduction from approximating the problem while respecting multiplicity constraints to approximating the problem with a bounded violation of the multiplicity constraints. 1 Research partially supported by NSERC Grant 22780900 and a CFI New Opportunities Award 1.
On Preemptive Resource Constrained Scheduling: Polynomialtime Approximation Schemes
, 2002
"... We study resource constrained scheduling problems where the objective is to compute feasible preemptive schedules minimizing the makespan and using no more resources than what are available. ..."
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Cited by 16 (9 self)
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We study resource constrained scheduling problems where the objective is to compute feasible preemptive schedules minimizing the makespan and using no more resources than what are available.
Approximating DisjointPath Problems Using Packing Integer Programs
, 1998
"... In a packing integer program, we are given a matrix A and column vectors b; c with nonnegative entries. We seek a vector x of nonnegative integers, which maximizes c^T x; subject to Ax ≤ b: The edge and vertexdisjoint path problems together with their unsplittable ow generalization are NPhard p ..."
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Cited by 15 (2 self)
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In a packing integer program, we are given a matrix A and column vectors b; c with nonnegative entries. We seek a vector x of nonnegative integers, which maximizes c^T x; subject to Ax ≤ b: The edge and vertexdisjoint path problems together with their unsplittable ow generalization are NPhard problems with a multitude of applications in areas such as routing, scheduling and bin packing. These two categories of problems are known to be conceptually related, but this connection has largely been ignored in terms of approximation algorithms. We explore the topic of approximating disjointpath problems using polynomialsize packing integer programs. Motivated by the...