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62
Approximation Algorithms for Connected Dominating Sets
 Algorithmica
, 1996
"... The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size, whe ..."
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Cited by 278 (9 self)
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The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size, where the graph induced by vertices in the dominating set is required to be connected as well. This problem arises in network testing, as well as in wireless communication. Two polynomial time algorithms that achieve approximation factors of O(H (\Delta)) are presented, where \Delta is the maximum degree, and H is the harmonic function. This question also arises in relation to the traveling tourist problem, where one is looking for the shortest tour such that each vertex is either visited, or has at least one of its neighbors visited. We study a generalization of the problem when the vertices have weights, and give an algorithm which achieves a performance ratio of 3 ln n. We also consider the ...
Improved Combinatorial Algorithms for the Facility Location and kMedian Problems
 In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science
, 1999
"... We present improved combinatorial approximation algorithms for the uncapacitated facility location and kmedian problems. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2:414 ..."
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Cited by 205 (13 self)
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We present improved combinatorial approximation algorithms for the uncapacitated facility location and kmedian problems. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2:414 + in ~ O(n 2 =) time. This also yields a bicriteria approximation tradeoff of (1 +; 1+ 2=) for facility cost versus service cost which is better than previously known tradeoffs and close to the best possible. Combining greedy improvement and cost scaling with a recent primal dual algorithm for facility location due to Jain and Vazirani, we get an approximation ratio of 1.853 in ~ O(n 3 ) time. This is already very close to the approximation guarantee of the best known algorithm which is LPbased. Further, combined with the best known LPbased algorithm for facility location, we get a very slight improvement in the approximation factor for facility location, achieving 1.728....
A polylogarithmic approximation algorithm for the group Steiner tree problem
 Journal of Algorithms
, 2000
"... The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich a ..."
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Cited by 129 (9 self)
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The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich and Widmayer and finds applications in VLSI design. The group Steiner tree problem generalizes the set covering problem, and is therefore at least as had. We give a randomized O(log 3 n log k)approximation algorithm for the group Steiner tree problem on an nnode graph, where k is the number of groups. The best previous ink)v/ (Bateman, Helvig, performance guarantee was (1 +  Robins and Zelikovsky).
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,
CostDistance: Two Metric Network Design
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the numbe ..."
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Cited by 59 (7 self)
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Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the number of sources. We reduce many common network design problems to CostDistance, obtaining (in some cases) the first known logarithmic approximation for them. These problems include singlesink buyatbulk with variable pipe types between different sets of nodes, facility location with buyatbulk type costs on edges, and maybecast with combind cost and distance metrics. Our algorithm is also the algorithm of choice for several previous network design problems, due to its ease of implementation and fast running time. 1 Introduction Consider designing a network from the ground up. We are given a set of customers, and need to place various servers and network links in order to cheaply provide sufficient service. If we only need to place the servers, this becomes the facility location problem and constantapproximations are known. If a single server handles all customers, and we impose the additional constraint that the set of available network link types is the same for every pair of nodes (subject to constant scaling factors on cost) then this is the single sink buyatbulk problem. We give the first known approximation for the general version of this problem with both servers and network links. We reduce the network design problem to an elegant theoretical framework: the CostDistance problem. We are given a graph with a single distinguished sink node (server). Every edge in this graph can be measured along two metrics; the first will be called cost and the second will be length. Note that the two metrics are entirely independent, and that there may be any number of parallel edges in the graph. We are given a set of sources (customers). Our objective is to construct a Steiner tree connecting the sources to the sink while minimizing the combined sum of the cost of the edges in the tree and sum over sources of the weighted length from source to sink.
Designing Networks with Bounded Pairwise Distance
"... We study the following network design problem: Given a communication network, find a minimum cost subset of missing links such that adding these links to the network makes every pair of points within distance at most d from each other. Theproblemhasbeenstudied earlier[17]undertheassumptionthatallli ..."
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Cited by 48 (0 self)
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We study the following network design problem: Given a communication network, find a minimum cost subset of missing links such that adding these links to the network makes every pair of points within distance at most d from each other. Theproblemhasbeenstudied earlier[17]undertheassumptionthatalllinkcostsas wellaslinklengthsareidentical,andwasshowntobe (logn)hardforeveryd4. Wepresentanovellinearprogrammingbasedapproachtoobtainan O(lognlogd)approximationalgorithmforthecaseofuniform linklengthsandcosts. We alsoextendthe(logn)hardnesstod2f2;3g. On the otherhand,iflinkcostscanvary, weshowthattheproblemis(2log1�n)hardford3. Thisversionofour problemcanbeviewedasaspecialcaseoftheminimum cost dspannerproblemandthusourhardnessresultappliesthereaswell. Ford=2,however,weshowthatthe problemcontinuestobeO(logn)approximablebygivingan O(logn)approximationtothemoregeneralminimumcost2spannerproblem.An(2log1�n)hardness resultalsoholdswhenalllinkcostsareidenticalbutlink lengthsmayvary(appliesevenwhenalllengthsare1or
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 45 (4 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.
A deterministic algorithm for the costdistance problem
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms
, 2001
"... The COSTDISTANCE network design problem is the following. We are given an undirected graph, a designated root vertex, and a set of terminals. We are also given two nonnegative real valued functions defined on, namely, a cost function and a length function, and a nonnegative weight function on the ..."
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Cited by 34 (0 self)
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The COSTDISTANCE network design problem is the following. We are given an undirected graph, a designated root vertex, and a set of terminals. We are also given two nonnegative real valued functions defined on, namely, a cost function and a length function, and a nonnegative weight function on the set. The goal is to find a tree that connects the terminals in to the root and minimizes!"$ # , where is the length of the path in from + to. We give a deterministic. 2435,/10 approximation algorithm for the COSTDISTANCE network design problem, in a sense derandomizing the algorithm given in [4]. Our algorithm is based on a natural 6/70)2835 linear programming relaxation of the problem and in the process we show that its integrality. gap is. Introduction: We study the COSTDISTANCE network design problem, recently defined by Meyerson,
On the Approximability of Some Network Design Problems
"... Consider the following classical network design problem: a set of terminals T: {t.i} wants to send traffic to a "root" r in an 'xnode graph G: (V, E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge e ca ..."
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Cited by 27 (3 self)
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Consider the following classical network design problem: a set of terminals T: {t.i} wants to send traffic to a "root" r in an 'xnode graph G: (V, E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge e can only be allocated in integral multiples of some base capacity ue and hence provisioning k x ue bandwidth on edge e incurs a cost of [k] times the cost of that edge. The objective is a minimumcost feasible solution. This is one of many network design problems widely studied where the bandwidth allocation being governed by side constraints: edges may only allow a subset of cables to be purchased on them, or certain qualityofservice requirements may have to be met. In this work, we show that the above problem, and in fact, several basic problems in this general network design framework, cannot be approximated better than ~(log log n) unless NP c _ OTIME(,r~°(l°gl°gl°gn)). In particular, we show that this inapproximability threshold holds for (i) the PrioritySteiner Tree problem [7], (ii) the CostDistance problem [31], and the singlesink version of an even more fundamental problem, (iii) Fixed Charge Network Flow [33]. Our results provide a further breakthrough in the understanding of the level of complexity of network design problems. These are the first nonconstant hardness results known for all these problems.
Approximation Algorithms for the Traveling Purchaser Problem and its Variants in Network Design
, 1999
"... . The traveling purchaser problem is a generalization of the traveling salesman problem with applications in a wide range of areas including network design and scheduling. The input consists of a set of markets and a set of products. Each market offers a price for each product and there is a cos ..."
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Cited by 24 (5 self)
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. The traveling purchaser problem is a generalization of the traveling salesman problem with applications in a wide range of areas including network design and scheduling. The input consists of a set of markets and a set of products. Each market offers a price for each product and there is a cost associated with traveling from one market to another. The problem is to purchase all products by visiting a subset of the markets in a tour such that the total travel and purchase costs are minimized. This problem includes many wellknown NPhard problems such as uncapacitated facility location, set cover and group Steiner tree problems as its special cases. We give an approximation algorithm with a polylogarithmic worstcase ratio for the traveling purchaser problem with metric travel costs. For a special case of the problem that models the ringstar network design problem, we give a constantfactor approximation algorithm. Our algorithms are based on rounding LP relaxation sol...