In recent years, many speed-up techniques for Dijkstra's algorithm have been developed that make the computation of shortest paths in static road networks a matter of microseconds. However, only few of those techn...
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In recent years, many speed-up techniques for Dijkstra's algorithm have been developed that make the computation of shortest paths in static road networks a matter of microseconds. However, only few of those techniques work in time-dependent networks which, unfortunately, appear quite frequently in reality: Roads are predictably congested by traffic jams, and efficient timetable information systems rely on time-dependent networks. Hence, a fast technique for routing in such networks is needed. In this work, we present an efficient time-dependent route planning algorithm. It is based on our recently introduced SHARC algorithm, which we adapt by augmenting its basic ingredients such that correctness can still be guaranteed in a time-dependent scenario. As a result, we are able to efficiently compute exact shortest paths in time-dependent continental-sized transportation networks, both of roads and of railways. It should be noted that time-dependent SHARC was the first efficient algorithm for time-dependent route planning.
For a graph G in read-only memory on n vertices and m edges and a write-only output buffer, we give two algorithms using only O(n) rewritable space. The first algorithm lists all minimal a - b separators of G with a p...
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For a graph G in read-only memory on n vertices and m edges and a write-only output buffer, we give two algorithms using only O(n) rewritable space. The first algorithm lists all minimal a - b separators of G with a polynomial delay of O(nm). The second lists all minimal vertex separators of G with a cumulative polynomial delay of O(n(3)m). One consequence is that the algorithms can list the minimal a - b separators (and minimal vertex separators) spending O(nm) time (respectively, O(n(3)m) time) per object output. (C) 2010 Elsevier B.V. All rights reserved.
An L(2. 1)-labeling of a graph G is an assignment of nonnegative integers, called colors, to the vertices of G such that the difference between the colors assigned to any two adjacent vertices is at least two and the ...
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An L(2. 1)-labeling of a graph G is an assignment of nonnegative integers, called colors, to the vertices of G such that the difference between the colors assigned to any two adjacent vertices is at least two and the difference between the colors assigned to any two vertices which are at distance two apart is at least one. The span of an L(2. 1)-labeling f is the maximum color number that has been assigned to a vertex of G by f. The L(2, 1)-labeling number of a graph G, denoted as lambda(G), is the least integer k such that G has an L(2, 1)-labeling of span k. In this paper, we propose a linear time algorithm to L(2, 1)-label a chain graph optimally. We present constant approximation L(2, 1)-labeling algorithms for various subclasses of chordal bipartite graphs. We show that lambda(G) = O(Delta(G)) for a chordal bipartite graph G, where Delta(G) is the maximum degree of G. However, we show that there are perfect elimination bipartite graphs having lambda = Omega(Delta(2)). Finally, we prove that computing lambda(C) of a perfect elimination bipartite graph is NP-hard. (C) 2010 Elsevier B.V. All rights reserved.
We give constant-factor approximation algorithms for computing the optimal branch-decompositions and largest grid minors of planar graphs. For a planar graph G with n vertices, let bw(G) be the branchwidth of G and gm...
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We give constant-factor approximation algorithms for computing the optimal branch-decompositions and largest grid minors of planar graphs. For a planar graph G with n vertices, let bw(G) be the branchwidth of G and gm(G) the largest integer g such that G has a g x g grid as a minor. Let c >= 1 be a fixed integer and alpha, beta arbitrary constants satisfying alpha > c + 1 and beta > 2c + 1. We give an algorithm which constructs in O(n(1+1/c) log n) time a branch-decomposition of G with width at most alpha bw(G). We also give an algorithm which constructs a g x g grid minor of G with g >= gm(G)/beta in O(n(1+1/c) log n) time. The constants hidden in the Big-O notations are proportional to c/alpha-(c+1) and c/beta-(2c+1), respectively. (C) 2010 Elsevier B.V. All rights reserved.
By a T-star we mean a complete bipartite graph K-1,K-t for some t = 2. Hell and Kirkpatrick devised an ad-hoc augmenting algorithm that finds a T-star packing covering the maximum number of nodes. The latter algorithm...
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ISBN:
(纸本)9783939897255
By a T-star we mean a complete bipartite graph K-1,K-t for some t <= T. For an undirected graph G, a T-star packing is a collection of node-disjoint T-stars in G. For example, we get ordinary matchings for T - 1 and packings of paths of length 1 and 2 for T - 2. Hereinafter we assume that T >= 2. Hell and Kirkpatrick devised an ad-hoc augmenting algorithm that finds a T-star packing covering the maximum number of nodes. The latter algorithm also yields a min-max formula. We show that T-star packings are reducible to network flows, hence the above problem is solvable in O(m root n) time (hereinafter n denotes the number of nodes in G, and m - the number of edges). For the edge-weighted case (in which weights may be assumed positive) finding a maximum T-packing is NP-hard. A novel 9 T/4 T+1-factor approximation algorithm is presented. For non-negative node weights the problem reduces to a special case of a max-cost flow. We develop a divide-and-conquer approach that solves it in O(m root n log n) time. The node-weighted problem with arbitrary weights is more difficult. We prove that it is NP-hard for T >= 3 and is solvable in strongly-polynomial time for T = 2.
In this paper we introduce a new graph class denoted as Gen(*;P-3, C-3, C-5). It contains all graphs that can be generated via split composition by using paths P-3 and cycles C-3 and C-5 as components. This new graph ...
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ISBN:
(纸本)9783642208775
In this paper we introduce a new graph class denoted as Gen(*;P-3, C-3, C-5). It contains all graphs that can be generated via split composition by using paths P-3 and cycles C-3 and C-5 as components. This new graph class extends the well known class of distance-hereditary graphs, which corresponds to Gen(*;P-3, C-3). For the new class we provide efficient algorithms for several basic combinatorial problems: recognition, stretch number, stability number, clique number, domination number, chromatic number, graph isomorphism, and clique width.
Novel analytical techniques have dramatically enhanced our understanding of many application domains including biological networks inferred from gene expression studies. However, there are clear computational challeng...
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ISBN:
(数字)9783642246692
ISBN:
(纸本)9783642246685
Novel analytical techniques have dramatically enhanced our understanding of many application domains including biological networks inferred from gene expression studies. However, there are clear computational challenges associated to the large datasets generated from these studies. The algorithmic solution of some NP-hard combinatorial optimization problems that naturally arise on the analysis of large networks is difficult without specialized computer facilities (i.e. supercomputers). In this work, we address the data clustering problem of large-scale biological networks with a polynomial-time algorithm that uses reasonable computing resources and is limited by the available memory. We have adapted and improved the MSTkNN graph partitioning algorithm and redesigned it to take advantage of external memory (EM) algorithms. We evaluate the scalability and performance of our proposed algorithm on a well-known breast cancer microarray study and its associated dataset.
Let G be a graph with n vertices and m edges. A sparsifier of G is a sparse graph on the same vertex set approximating G in some natural way. It allows us to say useful things about G while considering much fewer than...
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ISBN:
(纸本)9783939897255
Let G be a graph with n vertices and m edges. A sparsifier of G is a sparse graph on the same vertex set approximating G in some natural way. It allows us to say useful things about G while considering much fewer than m edges. The strongest commonly-used notion of sparsification is spectral sparsification;H is a spectral sparsifier of G if the quadratic forms induced by the Laplacians of G and H approximate one another well. This notion is strictly stronger than the earlier concept of combinatorial sparsification. In this paper, we consider a semi-streaming setting, where we have only (O) over tilde (n) storage space, and we thus cannot keep all of G. In this case, maintaining a sparsifier instead gives us a useful approximation to G, allowing us to answer certain questions about the original graph without storing all of it. In this paper, we introduce an algorithm for constructing a spectral sparsifier of G with O(n log n/epsilon(2)) edges (where epsilon is a parameter measuring the quality of the sparsifier), taking (O) over tilde (m) time and requiring only one pass over G. In addition, our algorithm has the property that it maintains at all times a valid sparsifier for the subgraph of G that we have received. Our algorithm is natural and conceptually simple. As we read edges of G, we add them to the sparsifier H. Whenever H gets too big, we resparsify it in (O) over tilde (n) time. Adding edges to a graph changes the structure of its sparsifier's restriction to the already existing edges. It would thus seem that the above procedure would cause errors to compound each time that we resparsify, and that we should need to either retain significantly more information or reexamine previously discarded edges in order to construct the new sparsifier. However, we show how to use the information contained in H to perform this resparsification using only the edges retained by earlier steps in nearly linear time.
We give constant-factor approximation algorithms for computing the optimal branch-decompositions and largest grid minors of planar graphs. For a planar graph G with n vertices, let bw(G) be the branchwidth of G and gm...
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ISBN:
(纸本)3642106307
We give constant-factor approximation algorithms for computing the optimal branch-decompositions and largest grid minors of planar graphs. For a planar graph G with n vertices, let bw(G) be the branchwidth of G and gm(G) the largest integer g such that G has a g x g grid as a minor. Let c >= 1 be a fixed integer and alpha, beta arbitrary constants satisfying alpha > c + 1 and beta > 2c + 1. We give an algorithm which constructs in O(n(1+1/c) log n) time a branch-decomposition of G with width at most alpha bw(G). We also give an algorithm which constructs a g x g grid minor of G with g >= gm(G)/beta in O(n(1+1/c) log n) time. The constants hidden in the Big-O notations are proportional to c/alpha-(c+1) and c/beta-(2c+1), respectively. (C) 2010 Elsevier B.V. All rights reserved.
graphs are high-dimensional, non-Euclidean data, whose utility spans a wide variety of disciplines. While their non-Euclidean nature complicates the application of traditional signal processing paradigms, it is desira...
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ISBN:
(纸本)9781457705700
graphs are high-dimensional, non-Euclidean data, whose utility spans a wide variety of disciplines. While their non-Euclidean nature complicates the application of traditional signal processing paradigms, it is desirable to seek an analogous detection framework. In this paper we present a matched filtering method for graph sequences, extending to a dynamic setting a previous method for the detection of anomalously dense subgraphs in a large background. In simulation, we show that this temporal integration technique enables the detection of weak subgraph anomalies than are not detectable in the static case. We also demonstrate background/foreground separation using a real background graph based on a computer network.
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