Ordered binary decision diagrams are a useful representation of Boolean functions, ii a good variable ordering is known. Variable orderings are computed by heuristic algorithms and then improved with local search and ...
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Ordered binary decision diagrams are a useful representation of Boolean functions, ii a good variable ordering is known. Variable orderings are computed by heuristic algorithms and then improved with local search and simulated annealing algorithms. This approach is based on the conjecture that the following problem is NP-complete. Given an OBDD G representing f and a size bound s, does there exist an OBDD G* (respecting an arbitrary variable ordering) representing with at most s nodes? This conjecture is proved.
This note presents a simple heuristic to speed up algorithms for the maximum flow problem that works by repeatedly finding blocking flows in layered (acyclic) networks. The heuristic assigns a capacity to each vertex ...
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This note presents a simple heuristic to speed up algorithms for the maximum flow problem that works by repeatedly finding blocking flows in layered (acyclic) networks. The heuristic assigns a capacity to each vertex of the layered network, which will be an upper bound on the amount of flow that can be transported through that vertex to the sink. This information can be utilized when constructing a blocking flow, since no vertex can ever accommodate more flow than its capacity. The static heuristic computes capacities in a layered network once, while a dynamic variant readjusts capacities during construction of the blocking flow. The effects of both static and dynamic heuristics are evaluated by a series of experiments with the wave algorithm of Tarjan. Although neither give theoretical improvement to the efficiency of the algorithm, the practical effects are in most cases worthwhile, and for certain types of networks quite dramatic.
In this paper, we give for constant k a linear-time algorithm that, given a graph G = (V, E), determines whether the treewidth of G is at most k and, if so, finds a tree-decomposition of G with treewidth at most k. A ...
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In this paper, we give for constant k a linear-time algorithm that, given a graph G = (V, E), determines whether the treewidth of G is at most k and, if so, finds a tree-decomposition of G with treewidth at most k. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at mast some constant k.
The Depth First Search (DFS) algorithm is one of the basic techniques that is used in a very large variety of graph algorithms. Most applications of the DFS involve the construction of a depth-first spanning tree (DFS...
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The Depth First Search (DFS) algorithm is one of the basic techniques that is used in a very large variety of graph algorithms. Most applications of the DFS involve the construction of a depth-first spanning tree (DFS tree). In this paper, we give a complete characterization of all the graphs in which every spanning tree is a DFS tree. These graphs are called Total-DFS-graphs. We prove that Total-DFS-graphs are closed under miners. it follows by the work of Robertson and Seymour on graph miners that there is a finite set of forbidden miners of these graphs and that there is a polynomial algorithm for their recognition. We also provide explicit characterizations of these graphs in terms of forbidden miners and forbidden topological miners. The complete characterization implies explicit linear algorithm for their recognition. In some problems the degree of some vertices in the DFS tree obtained in a certain run are crucial and therefore we also consider the following problem: Let G=(V, E) be a connected undirected graph where \V\ = n and let d is an element of N-n be a degree sequence upper bound vector. Is there any DFS tree T with degree sequence d(T) that violates d (i.e., d(T) not less than or equal to d, which means:,There Exists j such that d(T)(j) > d(j))? We show that this problem is NP-complete even for the case where we restrict the degree of only on specific vertex to be less than or equal to k for a fixed k greater than or equal to 2 (i.e., d = (n - 1,..., n - 1, k, n - 1,..., n - 1)). (C) 1995 John Wiley & Sons, Inc.
We introduce a new learning problem: learning a graph by piecemeal search, in which the learner must return every so often to its starting point (for refueling, say). We present two linear-time piecemeal-search algori...
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We introduce a new learning problem: learning a graph by piecemeal search, in which the learner must return every so often to its starting point (for refueling, say). We present two linear-time piecemeal-search algorithms for learning city-block graphs: grid graphs with rectangular obstacles.
We present a linear time algorithm for unit interval graph recognition. The algorithm is simple and based on Breadth-First Search. It is also direct - it does not first recognize the graph as an interval graph. Given ...
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We present a linear time algorithm for unit interval graph recognition. The algorithm is simple and based on Breadth-First Search. It is also direct - it does not first recognize the graph as an interval graph. Given a graph G, the algorithm produces an ordering of the vertices of the graph whenever G is a unit interval graph. This order corresponds to the order of the intervals of some unit interval model for G when arranged according to the increasing order of their left end coordinates. Breadth-First Search can also be used to construct a unit interval model for a unit interval graph on n vertices;in this model each endpoint is rational, with denominator n.
A quasi-median graph can be characterized as a weak retract of a Cartesian product of complete graphs or equivalently as a graph of finite winder. We derive a new characterization of quasi-median graphs which allows u...
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A quasi-median graph can be characterized as a weak retract of a Cartesian product of complete graphs or equivalently as a graph of finite winder. We derive a new characterization of quasi-median graphs which allows us to recognize these graphs in 0 (n root n log n + m log n) time. It is shown that skeletons of quasi-median graphs are median graphs. For an arbitrary vertex s an s-skeleton of a graph is obtained from G by deleting all edges uv that satisfy d(u, s) = d(v, s). As a by-product of this approach the size of a maximum complete subgraph of a quasi-median graph can be computed within the same time bound. Furthermore, we show that the distance matrix of a quasi-median graph can be computed in 0(n(2)).
A water-supply-distribution-system planning model has been developed using a directed graph algorithm as its pre- and postprocessors and a linear programming (LP) procedure as an ''intelligent'' system...
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A water-supply-distribution-system planning model has been developed using a directed graph algorithm as its pre- and postprocessors and a linear programming (LP) procedure as an ''intelligent'' system operator at its core. The directed graph, as a preprocessor, is used to produce a mathematical representation of the distribution system in question, to check the consistency and correctness of the network topology before an input file is created for the LP procedure. In the postprocessing mode, the directed graph generates files for graphical displays of model results and performs graph analyses such as depth- and breadth-first traversals, cut-set and connectivity for evaluating water-quality blending, tracking of source-to-demand contributions, system reliability, and lifeline objectives. Unlike the conventional formulation of a resource-allocation problem, the demand requirements, storage capacities, and other system constraints are removed from the constraint set and translated into a composite objective function. This methodology was successfully applied to the Metropolitan Water District of Southern California's (MWD's) distribution system. The results indicate that the combination of using an LP procedure and graph algorithm is a very versatile tool for solving large-scale water-distribution problems. This paper documents the concept used in developing the system-planning model and the results of its application to a simplified example as well as application to four case studies involving the entire MWD's distribution system.
We present an algorithm for maintaining the biconnected components of a graph during a sequence of edge insertions and deletions. It requires linear storage and preprocessing time. The amortized running time for inser...
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We present an algorithm for maintaining the biconnected components of a graph during a sequence of edge insertions and deletions. It requires linear storage and preprocessing time. The amortized running time for insertions and for deletions is O(m(2/3)), where m is the number of edges in the graph. Any query of the form 'Are the vertices u and v biconnected?' can be answered in time O(1). This is the first sublinear algorithm for this problem. We can also output all articulation points separating any two vertices efficiently. If the input is a plane graph, the amortized running time for insertions and deletions drops to O(root n log n) and the query time is O(log(2) n), where n is the number of vertices in the graph. The best previously known solution takes time O(n(2/3)) per update or query.
We give a simple algorithm to find a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous tradeoff: given the two trees and a gamma > ...
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We give a simple algorithm to find a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous tradeoff: given the two trees and a gamma > 0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortest-path tree is at most 1 + root 2 gamma times the shortest-path distance, and yet the total weight of the tree is at most 1 + root 2/gamma times the weight of a minimum spanning tree. Our algorithm runs in linear time and obtains the best-possible tradeoff. It can be implemented on a CREW PRAM to run a logarithmic time using one processor per vertex.
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