The long-term goal of this paper is to develop a robust simulator to study the EM scattering from vegetation. In an effort to overwhelm the intensive computational burden results from large sampling numbers, we decide...
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The long-term goal of this paper is to develop a robust simulator to study the EM scattering from vegetation. In an effort to overwhelm the intensive computational burden results from large sampling numbers, we decided to utilize the graphics Processing Unit (GPU), which has been greatly developed in recent years. In this paper, Compute Unified Device Architecture (CUDA) is combined with the four-path method to predict the EM scattering properties from scatterers which are sampled by using the Monte Carlo method in a two-layer canopy model. Obviously, a speedup of 77.8 times could be readily obtained in comparison with the original serial algorithm on a Core(TM) i5 CPU with the help of a GTS250 GPU as a coprocessor.
Given an edge-weighted undirected graph G and two prescribed vertices u and v, a next-to-shortest (u,v)-path is a shortest (u,v)-path amongst all (u,v)-paths having length strictly greater than the length of a shortes...
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Given an edge-weighted undirected graph G and two prescribed vertices u and v, a next-to-shortest (u,v)-path is a shortest (u,v)-path amongst all (u,v)-paths having length strictly greater than the length of a shortest (u,v)-path. In this paper, we deal with the problem of computing a next-to-shortest (u,v)-path. We propose an an O(n(2)) time algorithm for solving this problem, which significantly improves the bound of a previous one in O(n(3)) time where n is the number of vertices in G.
Let G be a directed acyclic graph (DAG). An upward (k, h)-topological book embedding of G is an upward book embedding on k pages of a subdivision of G where every edge is replaced by a path having at most h + 2 vertic...
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Let G be a directed acyclic graph (DAG). An upward (k, h)-topological book embedding of G is an upward book embedding on k pages of a subdivision of G where every edge is replaced by a path having at most h + 2 vertices. In this paper it is proved that every DAG with n vertices admits an upward (d + 1, 2inverted right perpendicularlog(d) ninverted left perpendicular -1)-topological book embedding, where d is any integer such that d >= 2. The result extends to the upward case well-known theorems for topological book embeddings of undirected graphs [H. Enomoto and M. S. Miyauchi, SIAM J. Discrete Math., 12 (1999), pp. 337-341], [M. S. Miyauchi, IEICE Transactions, 88-A (2005), pp. 1136-1139].
This paper introduces a novel approximation algorithm for the fundamental graph problem of combinatorial vector field topology (CVT). CVT is a combinatorial approach based on a sound theoretical basis given by Forman&...
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This paper introduces a novel approximation algorithm for the fundamental graph problem of combinatorial vector field topology (CVT). CVT is a combinatorial approach based on a sound theoretical basis given by Forman's work on a discrete Morse theory for dynamical systems. A computational framework for this mathematical model of vector field topology has been developed recently. The applicability of this framework is however severely limited by the quadratic complexity of its main computational kernel. In this work, we present an approximation algorithm for CVT with a significantly lower complexity. This new algorithm reduces the runtime by several orders of magnitude and maintains the main advantages of CVT over the continuous approach. Due to the simplicity of our algorithm it can be easily parallelized to improve the runtime further.
The problem of computing minimum distortion embeddings of a given graph into a line (path) was introduced in 2004 and has quickly attracted significant attention with subsequent results appearing at recent STOC and SO...
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The problem of computing minimum distortion embeddings of a given graph into a line (path) was introduced in 2004 and has quickly attracted significant attention with subsequent results appearing at recent STOC and SODA conferences. So far, all such results concern approximation algorithms or exponential-time exact algorithms. We give the first polynomial-time algorithms for computing minimum distortion embeddings of graphs into a path when the input graphs belong to specific graph classes. In particular, we solve this problem in polynomial time for bipartite permutation graphs and threshold graphs. For both graph classes, the distortion can be arbitrarily large. The graphs that we consider are unweighted. (C) 2011 Elsevier B.V. All rights reserved.
We present an approximation algorithm for the problem of finding a minimum set of edges in a given graph G whose removal from G leaves a graph in which each connected component is a path. It achieves a ratio of 10/7 a...
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We present an approximation algorithm for the problem of finding a minimum set of edges in a given graph G whose removal from G leaves a graph in which each connected component is a path. It achieves a ratio of 10/7 and runs in O(n (1.5)) time, where n is the number of vertices in the input graph. The previously best approximation algorithm for this problem achieves a ratio of 2 and runs in O(n (2)) time.
We present polynomial time algorithms for induced biclique optimization problems in the following families of graphs: polygon-circle graphs, 4-hole-free graphs, complements of interval-filament graphs and complements ...
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We present polynomial time algorithms for induced biclique optimization problems in the following families of graphs: polygon-circle graphs, 4-hole-free graphs, complements of interval-filament graphs and complements of subtree-filament graphs. Such problems are to find maximum: induced bicliques, induced balanced bicliques and induced edge bicliques. These problems have applications for biclique clustering of proteins by PPI criteria, of documents, and of web pages. (C) 2011 Elsevier B.V. All rights reserved.
The paper considers a team of robots which has to explore a graph G, where some nodes can be harmful. Robots are initially located at the so-called home base node. The dangerous nodes are the so-called black hole node...
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The paper considers a team of robots which has to explore a graph G, where some nodes can be harmful. Robots are initially located at the so-called home base node. The dangerous nodes are the so-called black hole nodes, and once a robot enters in one of them, it is destroyed. The goal is to find a strategy in order to explore Gin such a way that minimum number of robots is wasted. The exploration ends if there is at least one surviving robot which knows all the edges leading to the black holes. As many variations of the problem have been considered so far, the solution and its measure heavily depend on the initial knowledge and the capabilities of the robots. In this paper, we assume that G is a directed graph, the robots are associated with unique identifiers, they know the number of nodes n of G (or at least an upper bound on n), and they know the number of edges Delta leading to the black holes. Each node is associated with a whiteboard where robots can read and write information in a mutual exclusive way. A recently posed question [J. Czyzowicz, S. Dobrev, R. Kralovic, S. Miklik, D. Pardubska, Black hole search in directed graphs, in: Proc. of 16th International Colloquium on Structural Information and Communication Complexity, SIROCCO, LNCS, vol. 5869, 2009, pp. 182-194.] is whether some number of robots, expressed as a function of parameter Delta only, is sufficient to detect black holes in directed graphs of arbitrarily large order n. We give a positive answer to this question for the synchronous case, i.e., when the robots share a common clock, showing that O(Delta . 2(Delta)) robots are sufficient to solve the problem. This bound is nearly tight, since it is known that at least 2(Delta) robots are required for some instances. Quite surprisingly, we also show that unlike in the case of undirected graphs, for the directed version of the problem, synchronization can sometimes make a difference: for Delta = 2, in the synchronous case 4 robots are always suffici
We consider static ad hoc wireless networks whose nodes, equipped with the same initial battery charge, may dynamically change their transmission range. When a node v transmits with range r(v), its battery charge is d...
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We consider static ad hoc wireless networks whose nodes, equipped with the same initial battery charge, may dynamically change their transmission range. When a node v transmits with range r(v), its battery charge is decreased by beta r(v)(2), where beta > 0 is a fixed constant. The goal is to provide a range assignment schedule that maximizes the number of broadcast operations from a given source ( this number is denoted by the length of the schedule). This maximization problem, denoted by MAX LIFETIME, is known to be NP-hard and the best algorithm yields worst- case approximation ratio Theta(log n), where n is the number of nodes of the network. We consider random geometric instances formed by selecting n points independently and uniformly at random from a square of side length root n in the euclidean plane. We present an efficient algorithm that constructs a range assignment schedule having length not smaller than 1/12 of the optimum with high probability. Then we design an efficient distributed version of the above algorithm, where nodes initially know n and their own position only. The resulting schedule guarantees the same approximation ratio achieved by the centralized version, thus, obtaining the first distributed algorithm having provably good performance for this problem.
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover th...
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Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the universe with as few sets of the family as possible. The variations of covering problems include well-known problems like SET COVER, VERTEX COVER, DOMINATING SET and FACILITY LOCATION to name a few. Recently there has been a lot of study on partial covering problems, a natural generalization of covering problems. Here, the goal is not to cover all the elements but to cover the specified number of elements with the minimum number of sets. In this paper we study partial covering problems in graphs in the realm of parameterized complexity. Classical (non-partial) version of all these problems has been intensively studied in planar graphs and in graphs excluding a fixed graph H as a minor. However, the techniques developed for parameterized version of non-partial covering problems cannot be applied directly to their partial counterparts. The approach we use, to show that various partial covering problems are fixed parameter tractable on planar graphs, graphs of bounded local treewidth and graph excluding some graph as a minor, is quite different from previously known techniques. The main idea behind our approach is the concept of implicit branching. We find implicit branching technique to be interesting on its own and believe that it can be used for some other problems. (C) 2011 Elsevier Inc. All rights reserved.
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