We present a derivation of Dijkstra's shortest path algorithm [Numer. Math. 1 (1959) 83]. We view the problem as computation of a "greatest solution" of a set of equations. A UNITY-style computation [Cha...
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We present a derivation of Dijkstra's shortest path algorithm [Numer. Math. 1 (1959) 83]. We view the problem as computation of a "greatest solution" of a set of equations. A UNITY-style computation [Chandy and Misra, Parallel Program design: A Foundation, 1988] is then prescribed whose implementation results in Dijkstra's algorithm. (C) 2001 Elsevier Science B.V. All rights reserved.
Interval graphs are the intersection graphs of families of intervals in the real line. If the intervals can be chosen so that no interval contains another, we obtain the subclass of proper interval graphs. We show how...
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Interval graphs are the intersection graphs of families of intervals in the real line. If the intervals can be chosen so that no interval contains another, we obtain the subclass of proper interval graphs. We show how to recognize proper interval graphs in linear time by constructing the clique partition from the output of a single lexicographic breadth-first search.
We consider the problem of computing the Maximum Agreement Subtree (MAST) of a set of rooted leaf labeled trees. We give an algorithm which computes the MAST of k trees on n leaves where some tree has maximum outdegre...
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We consider the problem of computing the Maximum Agreement Subtree (MAST) of a set of rooted leaf labeled trees. We give an algorithm which computes the MAST of k trees on n leaves where some tree has maximum outdegree d in time O(kn(3) + n(d)).
This paper presents a method for statically inferring a range of information including strictness, evaluation-order, and evaluation-status information in a higher-order polymorphically-typed lazy functional language. ...
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This paper presents a method for statically inferring a range of information including strictness, evaluation-order, and evaluation-status information in a higher-order polymorphically-typed lazy functional language. This method is based on a compile-time analysis called order-of-demand analysis, which provides safe information about the order in which the values of bound variables are demanded. The time complexity of the analysis is substantially less than that of other approaches such as path analysis [5] and compositional analysis [7] and comparable to that of strictness analysis.
Channel routing is an important task in the layout design process of VLSI chips. In this paper, we study the channel routing problem on a hexagonal grid, which is composed of horizontal tracks, light tracks (with slop...
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Channel routing is an important task in the layout design process of VLSI chips. In this paper, we study the channel routing problem on a hexagonal grid, which is composed of horizontal tracks, light tracks (with slope +60 degrees), and left tracks (with slope -60 degrees). For a multiterminal channel routing problem with density d, we present a simple routing algorithm, which produces a layout in a channel of width w less than or equal to 2d + 1. This layout can be simply wired in three layers. It solves the open problem of three-layer wirability in [10].
Let G = (V, A) denote a simple connected directed graph, and let n = \V\, m = \A\, where n -1 less than or equal to m less than or equal to ((n)(2)). A feedback arc set (FAS) of G, denoted R(G), is a (possibly empty) ...
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Let G = (V, A) denote a simple connected directed graph, and let n = \V\, m = \A\, where n -1 less than or equal to m less than or equal to ((n)(2)). A feedback arc set (FAS) of G, denoted R(G), is a (possibly empty) set of arcs whose reversal makes G acyclic. A minimum feedback arc set of G, denoted R*(G), is a FAS of minimum cardinality r*(G);the computation of R*(G) is called the FAS problem. Berger and Shor have recently published an algorithm which, for a given digraph G, computes a FAS whose cardinality is at most m/2- c(1)m/Delta(1/2) where Delta is the maximum degree of G and Cl is a constant. Further, they exhibited an infinite class G of graphs with the property that for every G epsilon G and some constant C-2, r*(G)greater than or equal to m/2-c(2)m/Delta(1/2). Thus the Berger-Shor algorithm provides, in a certain asymptotic sense, an optimal solution to the FAS problem. Unfortunately, the Berger-Shor algorithm is complicated and requires running time 0(mn). In this paper we present a simple FAS algorithm which guarantees a good (though not optimal) performance bound and executes in time 0(m). Further, for the sparse graphs which arise frequently in graph drawing and other applications, our algorithm achieves the same asymptotic performance bound that Berger-Shor does.
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