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A general approximation technique for constrained forest problems
 in Proceedings of the 3rd Annual ACMSIAM Symposium on Discrete Algorithms
, 1992
"... Abstract. We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimizatio ..."
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Cited by 355 (21 self)
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Abstract. We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result is obtained for the 2matching problem and its variants. We also derive the first approximation algorithms for many NPcomplete problems, including the nonfixed pointtopoint connection problem, the exact path partitioning problem, and complex locationdesign problems. Moreover, for the prizecollecting traveling salesman or Steiner tree problems, we obtain 2approximation algorithms, therefore improving the previously bestknown performance guarantees of 2.5 and 3, respectively [Math. Programming, 59 (1993), pp. 413420].
Geometric Shortest Paths and Network Optimization
 Handbook of Computational Geometry
, 1998
"... Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of t ..."
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Cited by 147 (12 self)
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Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 123 (7 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
Computing MinimumWeight Perfect Matchings
 INFORMS
, 1999
"... We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the ..."
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Cited by 83 (2 self)
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We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dualchange � for each tree. As a benchmark of the algorithm’s performance, solving a 100,000node geometric instance on a 200 Mhz PentiumPro computer takes approximately 3 minutes.
New graph bipartizations for doubleexposure, bright field alternating phaseshift mask layout
 IN PROC. ASIA AND SOUTH PACIFIC DESIGN AUTOMATION CONFERENCE
, 2001
"... We describe new graph bipartization algorithms for layout modification and phase assignment of brightfield alternating phaseshifting masks (AltPSM) [25]. The problem of layout modification for phaseassignability reduces to the problem of making a certain layoutderived graph bipartite (i.e., 2col ..."
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Cited by 15 (2 self)
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We describe new graph bipartization algorithms for layout modification and phase assignment of brightfield alternating phaseshifting masks (AltPSM) [25]. The problem of layout modification for phaseassignability reduces to the problem of making a certain layoutderived graph bipartite (i.e., 2colorable). Previous work [3] solves bipartization optimally for the dark field alternating PSM regime. Only one degree of freedom is allowed (and relevant) for such a bipartization: edge deletion, which corresponds to increasing the spacing between features in order to remove phase conflict. Unfortunately, darkfield PSM is used only for contact layers, due to limitations of negative photoresists. Poly and metal layers are actually created using positive photoresists and brightfield masks. In this paper, we define a new graph bipartization formulation that pertains to the more technologically relevant brightfield regime. Previous work [3] does not apply to this regime. This formulation allows two degrees of freedom for layout perturbation: (i) increasing the spacing between features, and (ii) increasing the width of critical features. Each of these corresponds to node deletion in a new layoutderived graph that we define, called the feature graph. Graph bipartization by node deletion asks for a minimum weight node set A such that deletion of A makes the graph bipartite. Unlike bipartization by edge deletion, this problem is NPhard. We investigate several practical heuristics for the node deletion bipartization of planar graphs, including one that has 9/4 approximation ratio. Computational experience with industrial VLSI layout benchmarks shows promising results.
A Commercial Application of Survivable Network Design: ITP/INPLANS CCS Network Topology Analyzer
, 1996
"... ... Analyzer is a Bellcore product which performs automated design of cost effective survivable CCS (Common Channel Signaling) networks, with survivability meaning that certain pathconnectivity is preserved under limited failures of network elements. The algorithmic core of this product consists ..."
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Cited by 11 (0 self)
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... Analyzer is a Bellcore product which performs automated design of cost effective survivable CCS (Common Channel Signaling) networks, with survivability meaning that certain pathconnectivity is preserved under limited failures of network elements. The algorithmic core of this product consists of suitable extensions of primaldual approximation schemes for Steiner network problems. Even though most of the survivability problems arizing in CCS networks are not strictly of the form for which the approximation algorithms with proven performance guarantees apply, we implemented modifications of these algorithms with success: In addition to dualitybased performance guarantees that indicate, mathematically, discrepancy of no more than 20 % from optimal&y for generic Steiner problems and no more than 40% for survivable CCS networks, our software passed all commercial benchmark tests, and our code was deployed with the August ‘94 release of the product. CCS networks fall in the general category of low bitrate backbone networks. The main characteristic of survivability problems for these networks is that each edge, once present, can be as
On the semantics of Internet topologies
, 2002
"... Models for network topology are necessary for simulationbased studies of a variety of networking problems. Increasingly the research community is interested in problems that arise due to the large scale of the Internet (e.g., BGP routing, performance of peertopeer systems). For these sorts of pro ..."
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Cited by 6 (0 self)
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Models for network topology are necessary for simulationbased studies of a variety of networking problems. Increasingly the research community is interested in problems that arise due to the large scale of the Internet (e.g., BGP routing, performance of peertopeer systems). For these sorts of problems, the potential to model the fullscale ASlevel topology is appealing. To date, the most successful approach to modeling the ASlevel topology is the degreedriven approach of Inet. Inet predicts the degrees of the topology by extrapolation from available data, then constructs a topology meeting the degree sequence using a preferential connectivity heuristic. We focus on two important areas left open by prior work. First, we explore the theoretical foundations of degreebased graph generation. We identify the relevant results from graph theory, and exploit these to improve fundamental understanding and produce richer models. Second, essentially all prior ASlevel models have the characteristic that they contain extremely limited semantics. The graphs produced are undirected and unlabeled, hence they simply reect connectivity without any notion of additional semantic information. We address the issue of adding semantics to network topologies, in the areas of peering relationships and clustering into higherlevel groupings based on geographic and/or business relationships. Our techniques for adding semantics suggest new methods for evaluating the quality of generated topologies.
Approximation Algorithms for Minimumcost Lowdegree Subgraphs
, 2003
"... In this thesis we address problems in minimumcost lowdegree network design. In the design of communication networks we often face the problem of building a network connecting a large number of endhosts. Available hardware or software often imposes additional restrictions on the topology of the ne ..."
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Cited by 2 (0 self)
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In this thesis we address problems in minimumcost lowdegree network design. In the design of communication networks we often face the problem of building a network connecting a large number of endhosts. Available hardware or software often imposes additional restrictions on the topology of the network. One example for such a requirement arises in the area of computer networks: We are given a number of client hosts in a network that communicate with each other using a certain communication protocol that limits the number of simultaneously open connections for each host. In graph theoretic terms, where hosts correspond to nodes and network connections are represented by edges, this restriction naturally translates to a bound on the maximum nodedegree of the constructed network. In this thesis we first address the problem of finding a spanning tree T for a given undirected graph G = (V, E) with maximum nodedegree at most a given parameter B> 1. Among all such trees, we aim to find one that minimizes the total edgecost for a given cost function c on the edges of G. We develop an algorithm based on Lagrangean relaxation. We show how to compute a spanning tree with maximum nodedegree O(B + log(n)) and total cost at most a constant factor worse than the cost of
An Approximation Algorithm for MinimumCost VertexConnectivity Problems
"... Abstract. We present an approximation algorithm for solving graph problems in which a lowcost set of edges must be selected that has certain vertexconnectivity properties, in the survivable network design problem, a value ri) for each pair of vertices i and j is given, and a minimumcost set of ed ..."
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Abstract. We present an approximation algorithm for solving graph problems in which a lowcost set of edges must be selected that has certain vertexconnectivity properties, in the survivable network design problem, a value ri) for each pair of vertices i and j is given, and a minimumcost set of edges such that there are ri.i verlexdisjoint paths between vertices i and j must be found. In the case for which r 0 E 10. 1.2} for all i, j, we can find a solution of cost no more than three times the optimal cost in polynomial time. In the case in which rij = k for all i. j, we can find a solution of cost no more than 2~(k) times optimal, where 7~(nl = 1 + 89 +... + ~.. No approximation algorithms were previously known for these problems. Our algorithms rely on a primal~lual approach which has recently led to approximation algorithms for many edgeconnectivity problems. Key Words, Approximation algorithm, Vertex connectivity. Survivable network design, Primaldual method.