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Cuts, Trees and ℓ1Embeddings of Graphs
, 2002
"... Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into ℓ1 space. The main results are: 1. Explicit constantdistortion embeddings of all ..."
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Cited by 29 (8 self)
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Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into ℓ1 space. The main results are: 1. Explicit constantdistortion embeddings of all seriesparallel graphs, and all graphs with bounded Euler number. These are the first natural families known to have constant distortion (strictly greater than 1). Using the above embeddings, algorithms are obtained which approximate the sparsest cut in such graphs to within a constant factor. 2. A constantdistortion embedding of outerplanar graphs into the restricted class of ℓ1
Multicuts in Unweighted Graphs and Digraphs with Bounded Degree and Bounded TreeWidth
, 1998
"... this paper. Also, we show that Directed Edge Multicut is NPhard in digraphs with treewidth one and maximum in and out degree three. Other hardness results indicate why we cannot eliminate any of the three restrictionsunweighted, bounded degree and bounded treewidthon the input graph and sti ..."
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Cited by 24 (0 self)
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this paper. Also, we show that Directed Edge Multicut is NPhard in digraphs with treewidth one and maximum in and out degree three. Other hardness results indicate why we cannot eliminate any of the three restrictionsunweighted, bounded degree and bounded treewidthon the input graph and still obtain a PTAS. It is known [1] that for a Max SNPhard problem, unless P=NP, no PTAS exists. We have already seen that Unweighted Edge Multicut is Max SNPhard in stars [9], so letting the input graph have unbounded degree makes the problem harder. We show that Weighted Edge Multicut is Max SNPhard in binary trees, therefore letting the input graph be weighted makes the problem harder. Finally, we show that Unweighted Edge Multicut is Max SNPhard if the input graphs are walls. Walls, to be formally defined in Section 6, have degree at most three and unbounded treewidth. We conclude that letting the input graph have unbounded treewidth makes the problem significantly harder
PrimalDual Approximation Algorithms for Feedback Problems in Planar Graphs
 IPCO '96
, 1996
"... Given a subset of cycles of a graph, we consider the problem of finding a minimumweight set of vertices that meets all cycles in the subset. This problem generalizes a number of problems, including the minimumweight feedback vertex set problem in both directed and undirected graphs, the subset fee ..."
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Cited by 23 (3 self)
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Given a subset of cycles of a graph, we consider the problem of finding a minimumweight set of vertices that meets all cycles in the subset. This problem generalizes a number of problems, including the minimumweight feedback vertex set problem in both directed and undirected graphs, the subset feedback vertex set problem, and the graph bipartization problem, in which one must remove a minimumweight set of vertices so that the remaining graph is bipartite. We give a 9/4approximation algorithm for the general problem in planar graphs, given that the subset of cycles obeys certain properties. This results in 9/4approximation algorithms for the aforementioned feedback and bipartization problems in planar graphs. Our algorithms use the primaldual method for approximation algorithms as given in Goemans and Williamson [16]. We also show that our results have an interesting bearing on a conjecture of Akiyama and Watanabe [2] on the cardinality of feedback vertex sets in planar graphs.
Approximation algorithms for NPhard optimization problems
 In Algorithms and Theory of Computation Handbook
, 1999
"... Introduction In this chapter, we discuss approximation algorithms for optimization problems. An optimization problem consists in finding the best (cheapest, heaviest, etc.) element in a large set P , called the feasible region and usually specified implicitly, where the quality of elements of the se ..."
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Cited by 8 (0 self)
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Introduction In this chapter, we discuss approximation algorithms for optimization problems. An optimization problem consists in finding the best (cheapest, heaviest, etc.) element in a large set P , called the feasible region and usually specified implicitly, where the quality of elements of the set are evaluated using a function f(x), the objective function, usually something fairly simple. The element that minimizes (or maximizes) this function is said to be an optimal solution of the objective function at this element is the optimal value. optimal value = minff(x) j x 2 Pg (1) A example of an optimization problem familiar to computer scientists is that of finding a minimumcost spanning tree of a graph with edgecosts. For this problem, the feasible region P , the set over which we optimize, consists of spanning trees
Adversary Games in Secure/Reliable Network Routing
"... Abstract In this paper, we consider security aspects of network routing in a gametheoretic framework where an attacker is empowered with an ability for intrusion into edges of the network; on the other hand, the goal of designer is to choose routing paths. We interpret the secure routing problem a ..."
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Abstract In this paper, we consider security aspects of network routing in a gametheoretic framework where an attacker is empowered with an ability for intrusion into edges of the network; on the other hand, the goal of designer is to choose routing paths. We interpret the secure routing problem as a two player zero sum game. The attacker can choose one or more edges for intrusion, while the designer has to choose paths between sourcedestination pairs for a given set of pairs. We give polynomialtime algorithms for finding mixed Nash equilibria if 1) the attacker is limited to a oneedge attack, 2) the designer has two sourcedestination pairs while the attacker is either limited to c edges, for given c, or the attacker incurs a cost for each edge attacked. Previous work gave an algorithm for one sourcedestination pair and multiple edge attacks.
DYNAMIC DECISION MAKING FOR LESSTHANTRUCKLOAD TRUCKING OPERATIONS
, 2009
"... On a typical day, more than 53 million tons of goods valued at about $36 million are moved on the US multimodal transportation network. An efficient freight transportation industry is the key in facilitating the required movement of raw materials and finished products. Among different modes of trans ..."
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On a typical day, more than 53 million tons of goods valued at about $36 million are moved on the US multimodal transportation network. An efficient freight transportation industry is the key in facilitating the required movement of raw materials and finished products. Among different modes of transportation, trucking remains the shipping choice for many businesses and is increasing its market share. Lessthantruckload (LTL) trucking companies provide a transportation service in which several customers are served simultaneously by using the same truck and shipments need to be consolidated at some terminals to build economical loads. Intelligent transportation system (ITS) technologies increase the flow of available data, and offer opportunities to control the transportation operations in realtime. Some research efforts have considered realtime acceptance/rejection of shipping requests, but they are mostly focused on truckload trucking operations. This study tries to use realtime information in decision making for LTL carriers in a dynamically changing environment. The dissertation begins with an introduction of LTL trucking operations and