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56
Approximation Techniques for Utilitarian Mechanism Design
, 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 93 (5 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, we present a monotone PTAS for the generalized assignment problem with any bounded number of parameters per agent. The most efficient way to solve packing integer programs (PIPs) is LPbased randomized rounding, which also is in general not monotone. We show that primaldual greedy algorithms achieve almost the same approximation ratios for PIPs as randomized rounding. The advantage is that these algorithms are inherently monotone. This way, we can significantly improve the approximation ratios of truthful mechanisms for various fundamental mechanism design problems like singleminded combinatorial auctions (CAs), unsplittable flow routing and multicast routing. Our approximation algorithms can also be used for the winner determination in CAs with general bidders specifying their bids through an oracle.
Improved Bounds for the Unsplittable Flow Problem
 In Proceedings of the 13th ACMSIAM Symposium on Discrete Algorithms
, 2002
"... In this paper we consider the unsplittable ow problem (UFP): given a directed or undirected network G = (V, E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for eac ..."
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Cited by 56 (6 self)
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In this paper we consider the unsplittable ow problem (UFP): given a directed or undirected network G = (V, E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for each pair so that for every edge, the sum of the demands of the paths crossing the edge does not exceed its capacity.
The AllorNothing Multicommodity Flow Problem
 IN PROCEEDINGS OF THE 36TH ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC)
, 2004
"... ..., the same as that for edp [10]. Our algorithm extends to the case where each pair siti has a demand di associated with it and we need to completely route di to get credit for pair i. We also consider the online admission control version where pairs arrive online and the algorithm has to decide i ..."
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Cited by 43 (11 self)
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..., the same as that for edp [10]. Our algorithm extends to the case where each pair siti has a demand di associated with it and we need to completely route di to get credit for pair i. We also consider the online admission control version where pairs arrive online and the algorithm has to decide immediately on its arrival whether to accept it or not. We obtain a randomized algorithm with a competitive ratio that is similar to the approximation ratio for the offline algorithm.
Submodular function maximization via the multilinear relaxation and contention resolution schemes
 IN ACM SYMPOSIUM ON THEORY OF COMPUTING
, 2011
"... We consider the problem of maximizing a nonnegative submodular set function f: 2 N → R+ over a ground set N subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack constraints, and their intersections. In this paper we develop a general framework that all ..."
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Cited by 40 (2 self)
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We consider the problem of maximizing a nonnegative submodular set function f: 2 N → R+ over a ground set N subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack constraints, and their intersections. In this paper we develop a general framework that allows us to derive a number of new results, in particular when f may be a nonmonotone function. Our algorithms are based on (approximately) solving the multilinear extension F of f [5] over a polytope P that represents the constraints, and then effectively rounding the fractional solution. Although this approach has been used quite successfully in some settings [6, 22, 24, 13, 3], it has been limited in some important ways. We overcome these limitations as follows. First, we give constant factor approximation algorithms to maximize
B.: A quasiPTAS for unsplittable flow on line graphs
 In: STOC
, 2006
"... We study the Unsplittable Flow Problem (UFP) on a line graph, focusing on the longstanding open question of whether the problem is APXhard. We describe a deterministic quasipolynomial time approximation scheme for UFP on line graphs, thereby ruling out an APXhardness result, unless NP ⊆ DTIME(2 ..."
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Cited by 29 (3 self)
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We study the Unsplittable Flow Problem (UFP) on a line graph, focusing on the longstanding open question of whether the problem is APXhard. We describe a deterministic quasipolynomial time approximation scheme for UFP on line graphs, thereby ruling out an APXhardness result, unless NP ⊆ DTIME(2polylog(n)). Our result requires a quasipolynomial bound on all edge capacities and demands in the input instance. Earlier results on this problem included a polynomial time (2+ ε)approximation under the assumption that no demand exceeds any edge capacity (the “nobottleneck assumption”) and a superconstant integrality gap if this assumption did not hold. Unlike most earlier work on UFP, our results do not require a nobottleneck assumption.
A constant factor approximation algorithm for unsplittable flow on paths
 In Proceedings of the 52th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2011
, 2011
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Pricing on Paths: A PTAS for the Highway Problem
"... In the highway problem, we are given an nedge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the weight of the associated path, when it does not exceed the budg ..."
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Cited by 13 (1 self)
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In the highway problem, we are given an nedge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the weight of the associated path, when it does not exceed the budget of the driver, and zero otherwise. The goal is choosing weights so as to maximize the profit. A lot of research has been devoted to this apparently simple problem. The highway problem was shown to be strongly NPhard only recently [Elbassioni,Raman,Ray,Sitters’09]. The bestknown approximation is O(log n / log log n) [Gamzu,Segev’10], which improves on the previousbest O(log n) approximation [Balcan,Blum’06]. Better approximations are known for a number of special cases. Finding a constant (or better!) approximation algorithm for the general case is a challenging open problem. In this paper we present a PTAS for the highway problem, hence closing the complexity status of the problem. Our result is based on a novel randomized dissection approach, which has some points in common with Arora’s quadtree dissection for Euclidean network design [Arora’98]. The basic idea is enclosing the highway in a bounding path, such that both the size of the bounding path and the position of the highway in it are random variables. Then we consider a recursive O(1)ary dissection of the bounding path, in subpaths of uniform optimal weight. Since the optimal weights are unknown, we construct the dissection in a bottomup fashion via dynamic programming, while computing the approximate solution at the same time. Our algorithm can be easily derandomized. The same basic approach provides PTASs also for two generalizations of the problem: the tollbooth problem with a constant number of leaves and the maximumfeasibility subsystem problem on interval matrices. In both cases the previous best approximation factors are polylogarithmic [Gamzu,Segev’10,Elbassioni,Raman,Ray,Sitters’09].
The Demand Matching Problem
 In Proceedings of the 9th International Conference on Integer Programming and Combinatorial Optimization (IPCO
, 2002
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Algorithms for FaultTolerant Routing in Circuit Switched Networks (Extended Abstract)
 In Proceedings of 14th Annual ACM Symposium on Parallel Algorithms and Architectures
, 2002
"... Amitabha Bagchi, Amitabh Chaudhary, and Christian Scheideler Dept. of Computer Science Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218, USA {bagchi,amic,scheideler}@cs.jhu.edu Petr Kolman Inst. for Theoretical Computer Science Charles University Malostransk e n am. 25 1 ..."
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Cited by 10 (3 self)
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Amitabha Bagchi, Amitabh Chaudhary, and Christian Scheideler Dept. of Computer Science Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218, USA {bagchi,amic,scheideler}@cs.jhu.edu Petr Kolman Inst. for Theoretical Computer Science Charles University Malostransk e n am. 25 118 00 Prague, Czech Republic kolman@kam.mff.cuni.cz ABSTRACT In this paper we consider the k edgedisjoint paths problem (kEDP), a generalization of the wellknown edgedisjoint paths problem. Given a graph G = (V, E) and a set of terminal pairs (or requests) T , the problem is to find a maximum subset of the pairs in T for which it is possible to select paths such that each pair is connected by k edgedisjoint paths and the paths for di#erent pairs are mutually disjoint. To the best of our knowledge, no nontrivial result is known for this problem for k > 1. To measure the performance of our algorithms we will use the recently introduced flow number F of a graph. This parameter is known to fulfill F = O(## 1 log n), where # is the maximum degree and # is the edge expansion of G. We show that a simple, greedy online algorithm achieves a competitive ratio of F ), which naturally extends the best known bound of O(F ) for k = 1 to higher k. To achieve this competitive ratio, we introduce a new method of converting a system of k disjoint paths into a system of k lengthbounded disjoint paths. We also show that any deterministic online algorithm has a competitive ratio of ## k F ).