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Approximating the SingleSink Link Installation Problem in Network Design
, 1998
"... We initiate the algorithmic study of an important but NPhard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem v , for each source node v. (2) ..."
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Cited by 45 (2 self)
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We initiate the algorithmic study of an important but NPhard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem v , for each source node v. (2) A small set of cable types, where each cable type is specified by its capacity and its cost per unit length. The cost per unit capacity per unit length of a highcapacity cable may be significantly less than that of a lowcapacity cable, reflecting an economy of scale, i.e., the payoff for buying at bulk may be very high. The goal is to design a minimumcost network that can (simultaneously) route all the demands at the sources to the sink, by installing zero or more copies of each cable type on each edge of the graph. An additional restriction is that the demand of each source must follow a single path. The problem is to find a route from each source node to the sink and to assign ca...
Rounding to an integral program
 In Proceedings of the 4th International Workshop on Efficient and Experimental Algorithms (WEA’05
, 2005
"... Abstract. We present a general framework for approximating several NPhard problems that have two underlying properties in common. First, the problems we consider can be formulated as integer covering programs, possibly with additional side constraints. Second, the number of covering options is rest ..."
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Cited by 11 (0 self)
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Abstract. We present a general framework for approximating several NPhard problems that have two underlying properties in common. First, the problems we consider can be formulated as integer covering programs, possibly with additional side constraints. Second, the number of covering options is restricted in some sense, although this property may be well hidden. Our method is a natural extension of the threshold rounding technique. 1
Instant Recognition of Half Integrality and 2Approximations
 In Proceedings of the 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization
, 1998
"... . We define a class of integer programs with constraints that involve up to three variables each. A generic constraint in such integer program is of the form ax + by z + c, where the variable z appears only in that constraint. For such binary integer programs it is possible to derive half integral ..."
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Cited by 8 (0 self)
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. We define a class of integer programs with constraints that involve up to three variables each. A generic constraint in such integer program is of the form ax + by z + c, where the variable z appears only in that constraint. For such binary integer programs it is possible to derive half integral superoptimal solutions in polynomial time. The scheme is also applicable with few modifications to nonbinary integer problems. For some of these problems it is possible to round the half integral solution to a 2approximate solution. This extends the class of integer programs with at most two variables per constraint that were analyzed in [HMNT93]. The approximation algorithms here provide an improvement in running time and range of applicability compared to existing 2approximations. Furthermore, we conclude that problems in the framework are MAX SNPhard and at least as hard to approximate as vertex cover. Problems that are amenable to the analysis provided here are easily recognized. The ...
Parameterized Complexity Dichotomy for Steiner Multicut (Full Version)
, 2014
"... We consider the Steiner Multicut problem, which asks, given an undirected graph G, a collection T = {T1,..., Tt}, Ti ⊆ V (G), of terminal sets of size at most p, and an integer k, whether there is a set S of at most k edges or nodes such that of each set Ti at least one pair of terminals is in diffe ..."
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We consider the Steiner Multicut problem, which asks, given an undirected graph G, a collection T = {T1,..., Tt}, Ti ⊆ V (G), of terminal sets of size at most p, and an integer k, whether there is a set S of at most k edges or nodes such that of each set Ti at least one pair of terminals is in different connected components of G \S. This problem generalizes several wellstudied graph cut problems, in particular the Multicut problem, which corresponds to the case p = 2. The Multicut problem was recently shown to be fixedparameter tractable for the parameter k [Marx and Razgon, Bousquet et al., STOC 2011]. The question whether this result generalizes to Steiner Multicut motivates the present work. We answer the question that motivated this work, and in fact provide a dichotomy of the parameterized complexity of Steiner Multicut on general graphs. That is, for any combination of k, t, p, and the treewidth tw(G) as constant, parameter, or unbounded, and for all versions of the problem (edge deletion and node deletion with and without deletable terminals), we prove either that the problem is fixedparameter tractable or that the problem is hard (W[1]hard or even (para)NPcomplete). Among the many results in the paper,
Approximating the SingleSink Edge Installation Problem in Network Design
, 1997
"... We initiate the algorithmic study of an important but NPhard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem v , for each source node v. (2) A s ..."
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We initiate the algorithmic study of an important but NPhard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem v , for each source node v. (2) A small set of cable types, where each cable type is specified by its capacity and its cost per unit length. The cost per unit capacity per unit length of a highcapacity cable may be significantly less than that of a lowcapacity cable, reflecting an economy of scale, i.e., the payoff for buying at bulk may be very high. The goal is to design a minimumcost network that can (simultaneously) route all the demands at the sources to the sink, by installing zero or more copies of each cable type on each edge of the graph. An additional restriction is that the demand of each source must follow a single path. Thus, the problem is to find a route for each sink node and to assign capacity to each edge...