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47
Depth first search and linear graph algorithms
 SIAM Journal on Computing
, 1972
"... Abstract. The value of depthfirst search or "bacltracking " as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of ..."
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Cited by 1015 (12 self)
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Abstract. The value of depthfirst search or "bacltracking " as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of an undirect graph are presented. The space and time requirements of both algorithms are bounded by k 1V + k2E d k for some constants kl, k2, and k a, where Vis the number of vertices and E is the number of edges of the graph being examined.
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 394 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which finds such a partition A, B, C in O(n) time.
Efficient planarity testing
 J. Assoc. Comput. Mach
, 1974
"... ABSTRACT. This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm uses depthfi ..."
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Cited by 227 (5 self)
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ABSTRACT. This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm uses depthfirst search and has O(V) time and space bounds, where V is the number of vertices in G. An ALGOS implementation of the algorithm successfully tested graphs with as many as 900 vertices in less than 12 seconds.
Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms
 SIAM JOURNAL ON COMPUTING
, 1989
"... We assume a parallel RAM model which allows both concurrent reads and concurrent writes of a global memory. Our main result is an optimal randomized parallel algorithm for INTEGER SORT (i.e., for sorting n integers in the range [1; n]). Our algorithm costs only logarithmic time and is the first know ..."
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Cited by 62 (12 self)
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We assume a parallel RAM model which allows both concurrent reads and concurrent writes of a global memory. Our main result is an optimal randomized parallel algorithm for INTEGER SORT (i.e., for sorting n integers in the range [1; n]). Our algorithm costs only logarithmic time and is the first known that is optimal: the product of its time and processor bounds is upper bounded by a linear function of the input size. We also give a deterministic sublogarithmic time algorithm for prefix sum. In addition we present a sublogarithmic time algorithm for obtaining a random permutation of n elements in parallel. And finally, we present sublogarithmic time algorithms for GENERAL SORT and INTEGER SORT. Our sublogarithmic GENERAL SORT algorithm is also optimal.
Distributed covering by antrobots using evaporating traces
 IEEE Transactions on Robotics and Automation
, 1999
"... Abstract—Ants and other insects are known to use chemicals called pheromones for various communication and coordination tasks. In this paper, we investigate the ability of a group of robots, that communicate by leaving traces, to perform the task of cleaning the floor of an unmapped building, or an ..."
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Cited by 59 (1 self)
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Abstract—Ants and other insects are known to use chemicals called pheromones for various communication and coordination tasks. In this paper, we investigate the ability of a group of robots, that communicate by leaving traces, to perform the task of cleaning the floor of an unmapped building, or any task that requires the traversal of an unknown region. More specifically, we consider robots which leave chemical odor traces that evaporate with time, and are able to evaluate the strength of smell at every model is a decentralized multiagent adaptive system with a shared memory, moving on a graph whose vertices are the floortiles. We describe three methods of covering a graph in a distributed fashion, using smell traces that gradually vanish with time, and show that they all result in eventual task completion, two of them in a time polynomial in the number of tiles. As opposed to existing traversal methods (e.g., depth first search), our algorithms are adaptive: they will complete the traversal of the graph even if some of the a(ge)nts die or the graph changes (edges/vertices added or deleted) during the execution, as long as the graph stays connected. Another advantage of our agent interaction processes is the ability of agents to use noisy information at the cost of longer cover time. Index Terms—Antrobotics, covering, exploration, multiagent systems, robotics.
Data flow analysis in software reliability
 ACM Computing Surveys
, 1976
"... The ways that the methods of data flow analysis can be applied to improve software reliability are described. There is also a review of the basic terminology from graph theory and from data flow analysis in global program optimization. The notation of regular expressions is used to describe actions ..."
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Cited by 44 (0 self)
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The ways that the methods of data flow analysis can be applied to improve software reliability are described. There is also a review of the basic terminology from graph theory and from data flow analysis in global program optimization. The notation of regular expressions is used to describe actions on data for sets of paths.
Numerical Experiments with Iteration and Aggregation for Markov Chains
 ORSA Journal on Computing
, 1996
"... This paper describes an iterative aggregation/disaggregation method for computing the stationary probability vector of a nearly completely decomposable Markov chain. The emphasis is on the implementation of the algorithm and on the results that are obtained when it is applied to three modelling exam ..."
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Cited by 27 (8 self)
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This paper describes an iterative aggregation/disaggregation method for computing the stationary probability vector of a nearly completely decomposable Markov chain. The emphasis is on the implementation of the algorithm and on the results that are obtained when it is applied to three modelling examples that have been used in the analysis of computer/communication systems. Where applicable, a comparison with standard iterative and direct methods for solving the same problems, is made. Key words: Large Markov Chain Models; NearCompleteDecomposability; Iteration and Aggregation; Numerical Experiments. Research supported in part by NSF (DDM8906248) Introduction Let Q be the infinitesimal generator of an irreducible continuoustime Markov chain and let ß be its stationary probability vector. Thus q ij denotes the rate of transition from state i to state j; q ii = \Gamma P j 6=i q ij and ß i is the probability that the system is in state i at statistical equilibrium. It may be sho...
Efficiently Searching a Graph by a SmellOriented Vertex Process
 Annals of Mathematics and Artificial Intelligence
, 1998
"... Efficient graph search is a central issue in many aspects of AI. In most of existing work there is a distinction between the active "searcher", which both executes the algorithm and holds the memory, and the passive "searched graph", over which the searcher has no ..."
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Cited by 20 (3 self)
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Efficient graph search is a central issue in many aspects of AI. In most of existing work there is a distinction between the active &quot;searcher&quot;, which both executes the algorithm and holds the memory, and the passive &quot;searched graph&quot;, over which the searcher has no control at all. Large dynamic networks like the Internet, where the nodes are powerful computers and the links have narrow band and are heavilyloaded, call for a different paradigm, in which most of the burden of computing and memorizing is moved from the searching agent to the nodes of the network. In this paper we suggest a method for searching an undirected, connected graph using the VertexAntWalk method, where an a(ge)nt walks along the edges of a graph G, occasionally leaving &quot;pheromone &quot; traces at nodes, and using those traces to guide its exploration. We show that the ant can cover the graph within time O(nd) where n is the number of vertices and d the diameter of G. The use of traces achieves a tradeoff between random and selfavoiding walks, as it dictates a lower priority for alreadyvisited neighbors. Further properties of
Numerical Methods for Computing Stationary Distributions of Finite Irreducible Markov Chains
 of Advances in Computational Probability
, 1997
"... Introduction In this chapter our attention will be devoted to computational methods for computing stationary distributions of finite irreducible Markov chains. We let q ij denote the rate at which an nstate Markov chain moves from state i to state j. The n \Theta n matrix Q whose offdiagonal ele ..."
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Cited by 16 (0 self)
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Introduction In this chapter our attention will be devoted to computational methods for computing stationary distributions of finite irreducible Markov chains. We let q ij denote the rate at which an nstate Markov chain moves from state i to state j. The n \Theta n matrix Q whose offdiagonal elements are q ij and whose i th diagonal element is given by \Gamma P n j=1;j 6=i q ij is called the infinitesimal generator of the Markov chain. It may be shown that the stationary probability vector ß, a row vector whose kth element denotes the stationary probability of being in state k, can be obtained by solving the homogeneous system of equations ßQ<F34
The SONET EdgePartition Problem
 Networks
, 2002
"... Motivated by a problem arising in the design of telecommunications networks using the SONET standard, we consider the problem of covering all edges of a graph using subgraphs that contain at most k edges with the objective of minimizing the total number of vertices in the subgraphs. We show that the ..."
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Cited by 15 (1 self)
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Motivated by a problem arising in the design of telecommunications networks using the SONET standard, we consider the problem of covering all edges of a graph using subgraphs that contain at most k edges with the objective of minimizing the total number of vertices in the subgraphs. We show that the problem is NPhard when k 3 and present a lineartime approximation algorithm. For even k values we present an approximation scheme with a reduced ratio but with increased complexity.