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38
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 127 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
A Better Heuristic for Orthogonal Graph Drawings
 COMPUT. GEOM. THEORY APPL
, 1998
"... An orthogonal drawing of a graph is an embedding in the plane such that all edges are drawn as sequences of horizontal and vertical segments. We present a linear time and space algorithm to draw any connected graph orthogonally on a grid of size n \Theta n with at most 2n + 2 bends. Each edge is ben ..."
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Cited by 61 (6 self)
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An orthogonal drawing of a graph is an embedding in the plane such that all edges are drawn as sequences of horizontal and vertical segments. We present a linear time and space algorithm to draw any connected graph orthogonally on a grid of size n \Theta n with at most 2n + 2 bends. Each edge is bent at most twice. In particular for nonplanar and nonbiconnected planar graphs, this is a big improvement. The algorithm is very simple, easy to implement, and it handles both planar and nonplanar graphs at the same time.
Disjoint Paths in Densely Embedded Graphs
 in Proceedings of the 36th Annual Symposium on Foundations of Computer Science
, 1995
"... We consider the following maximum disjoint paths problem (mdpp). We are given a large network, and pairs of nodes that wish to communicate over paths through the network  the goal is to simultaneously connect as many of these pairs as possible in such a way that no two communication paths share a ..."
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Cited by 60 (6 self)
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We consider the following maximum disjoint paths problem (mdpp). We are given a large network, and pairs of nodes that wish to communicate over paths through the network  the goal is to simultaneously connect as many of these pairs as possible in such a way that no two communication paths share an edge in the network. This classical problem has been brought into focus recently in papers discussing applications to routing in highspeed networks, where the current lack of understanding of the mdpp is an obstacle to the design of practical heuristics. We consider the class of densely embedded, nearlyEulerian graphs, which includes the twodimensional mesh and many other planar and locally planar interconnection networks. We obtain a constantfactor approximation algorithm for the maximum disjoint paths problem for this class of graphs; this improves on an O(log n)approximation for the special case of the twodimensional mesh due to AumannRabani and the authors. For networks that ...
OnLine Randomized Call Control Revisited
 SIAM J. COMPUTING
, 2001
"... We consider the problem of online call admission and routing on trees and meshes. Previous work gave randomized online algorithms for these problems and proved that they have optimal (up to constant factors) competitive ratios. However, these algorithms can obtain very low profit with high probabi ..."
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Cited by 32 (8 self)
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We consider the problem of online call admission and routing on trees and meshes. Previous work gave randomized online algorithms for these problems and proved that they have optimal (up to constant factors) competitive ratios. However, these algorithms can obtain very low profit with high probability. We investigate the question of devising for these problems online competitive algorithms that also guarantee a "good" solution with "good" probability. We give a new
Packing Steiner Trees: A Cutting Plane Algorithm and Computational Results
 Mathematical Programming
, 1992
"... In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSIdesign and report on our computational experience. This includes a brief discussion of separation algorithms, a new LPbased primal heuristi ..."
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Cited by 31 (12 self)
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In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSIdesign and report on our computational experience. This includes a brief discussion of separation algorithms, a new LPbased primal heuristic and implementation details. The paper is based on the polyhedral theory for the Steiner tree packing polyhedron developed in our companion paper [GMW92] and meant to turn this theory into an algoritmic tool for the solution of practical problems.
On Linear Layouts of Graphs
, 2004
"... In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A kstack (resp... ..."
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Cited by 31 (19 self)
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In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A kstack (resp...
A Survey on MultiNet Global Routing for Integrated Circuits
 Integration, the VLSI Journal
, 2001
"... This paper presents a comprehensive survey on global routing research over about the last two decades, with an emphasis on the problems of simultaneously routing multiple nets in VLSI circuits under various design styles. The survey begins with a coverage of traditional approaches such as sequential ..."
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Cited by 24 (2 self)
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This paper presents a comprehensive survey on global routing research over about the last two decades, with an emphasis on the problems of simultaneously routing multiple nets in VLSI circuits under various design styles. The survey begins with a coverage of traditional approaches such as sequential routing and ripupandreroute, and then discusses multicommodity flow based methods, which have attracted a good deal of attention recently. The family of hierarchical routing techniques and several of its variants are then overviewed, in addition to other techniques such as movebased heuristics and iterative deletion. While many traditional techniques focus on the conventional objective of managing congestion, newer objectives have come into play with the advances in VLSI technology. Specifically, the focus of global routing has shifted so that it is important to augment the congestion objective with metrics for timing and crosstalk. In the later part of this paper, we summarize the recent progress in these directions. Finally, the survey concludes with a summary of
Planar Polyline Drawings with Good Angular Resolution
 Graph Drawing (Proc. GD '98), volume 1547 of LNCS
, 1998
"... . We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree d on a (2n \Gamma 5) \Theta ( 3 2 n \Gamma 7 2 ) grid with at most 5n \Gamma 15 bends and minimum angle ? 2 d . In the constructed drawings, every edge h ..."
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Cited by 22 (1 self)
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. We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree d on a (2n \Gamma 5) \Theta ( 3 2 n \Gamma 7 2 ) grid with at most 5n \Gamma 15 bends and minimum angle ? 2 d . In the constructed drawings, every edge has at most three bends and length O(n). To our best knowledge, this algorithm achieves the best simultaneous bounds concerning the grid size, angular resolution, and number of bends for planar grid drawings of highdegree planar graphs. Besides the nice theoretical features, the practical drawings are aesthetically very pleasing. An implementation of our algorithm is available with the AGDLibrary (Algorithms for Graph Drawing) [2, 1]. Our algorithm is based on ideas by Kant for polyline grid drawings for triconnected plane graphs [23]. In particular, our algorithm significantly improves upon his bounds on the angular resolution and the grid size for nontriconnected plane graphs....
Routing Through Virtual Paths in Layered Telecommunication Networks
, 1995
"... We study a network configuration problem in telecommunications where one wants to set up paths in a capacitated network to accommodate given pointtopoint traffic demand. The problem is formulated as an integer linear programming model where 01 variables represent different paths. An associated in ..."
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Cited by 15 (1 self)
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We study a network configuration problem in telecommunications where one wants to set up paths in a capacitated network to accommodate given pointtopoint traffic demand. The problem is formulated as an integer linear programming model where 01 variables represent different paths. An associated integral polytope is studied and different classes of facets are described. These results are used in a cutting plane algorithm. Computational results for some realistic problems are reported. 1 This research was supported by Telenor Research and Development (Project number TFN9506A). 2 University of Oslo, P.O.Box 1080, Blindern, N0316 Oslo, Norway. Email: geird@ifi.uio.no. 3 KonradZuseZentrum fur Informationstechnik, Heilbronner Str. 10, D10711 Berlin, Germany. Email: martin@zibberlin.de. 4 Telenor Research and Development, P.O.Box 83, N2007 Kjeller, Norway. Email: stoer@nta.no. 1 Introduction A major trend in telecommunications is increased flexibility in terms of network con...