Routing and wavelength assignment (RWA) aims to assign the limited number of wavelengths in a wavelength-division multiplexed (WDM) optical network so as to achieve greater capacity. In a recent paper [6], Datta etal....
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Routing and wavelength assignment (RWA) aims to assign the limited number of wavelengths in a wavelength-division multiplexed (WDM) optical network so as to achieve greater capacity. In a recent paper [6], Datta etal. studied the problem of establishing a set of disjoint lightpaths on a tree topology using a single wavelength to maximize the total traffic supported by the chosen set of lightpaths. They discussed applications of this problem to RWA and presented a dynamic programming algorithm which optimally solves this problem in O(n(4) +nD(3)) time, where n is the number of nodes in the network and D is the maximum node degree. In this paper, we present an improved algorithm with a time complexity of O(n(2) + nD(2)).
A graph G is the k-leaf power of a tree T if its vertices are leaves of T such that two vertices are adjacent in G if and only if their distance in T is at most k. Then T is the k-leaf root of G. This notion was intro...
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A graph G is the k-leaf power of a tree T if its vertices are leaves of T such that two vertices are adjacent in G if and only if their distance in T is at most k. Then T is the k-leaf root of G. This notion was introduced and studied by Nishimura, Ragde, and Thilikos motivated by the search for underlying phylogenetic trees. Their results imply a O(n(3)) time recognition algorithm for 3-leaf powers. Later, Dom, Guo, Huffner, and Niederineier characterized 3-leaf powers as the (bull. dart, gem)-free chordal graphs. We show that a connected graph is a 3-leaf power if and only if it results from substituting cliques into the vertices of a tree. This characterization is much simpler than the previous characterizations via critical cliques and forbidden induced subgraphs and also leads to linear time recognition of these graphs. (c) 2006 Elsevier B.V. All rights reserved.
We study an NP-hard (and MaxSNP-hard) problem in trees-MULTICOMMODITY DEMAND FLOW-dealing with demand flows between pairs of nodes and trying to maximize the value of the routed flows. This problem has been intensivel...
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We study an NP-hard (and MaxSNP-hard) problem in trees-MULTICOMMODITY DEMAND FLOW-dealing with demand flows between pairs of nodes and trying to maximize the value of the routed flows. This problem has been intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomial-time approximation algorithms. By way of contrast, we provide an exact dynamic programming algorithm for this problem that works well whenever some natural problem parameter is small, a reasonable assumption in several applications. More specifically, we prove fixed-parameter tractability with respect to the maximum number of the input flows at any tree node. (c) 2005 Elsevier B.V. All rights reserved.
algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper, we focus on the recent technique proposed by Wainwright et al. [33]-tree-reweighted max-product message pass...
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algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper, we focus on the recent technique proposed by Wainwright et al. [33]-tree-reweighted max-product message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy. However, the algorithm is not guaranteed to increase this bound-it may actually go down. In addition, TRW does not always converge. We develop a modification of this algorithm which we call sequential tree-reweighted message passing. Its main property is that the bound is guaranteed not to decrease. We also give a weak tree agreement condition which characterizes local maxima of the bound with respect to TRW algorithms. We prove that our algorithm has a limit point that achieves weak tree agreement. Finally, we show that, our algorithm requires half as much memory as traditional message passing approaches. Experimental results demonstrate that on certain synthetic and real problems, our algorithm outperforms both the ordinary belief propagation and tree-reweighted algorithm in [33]. In addition, on stereo problems with Potts interactions, we obtain a lower energy than graph cuts.
In the context of graph transformation we look at the operation of switching, which can be viewed as a method for realizing global transformations of (group-labelled) graphs through local transformations of the vertic...
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In the context of graph transformation we look at the operation of switching, which can be viewed as a method for realizing global transformations of (group-labelled) graphs through local transformations of the vertices. In case vertices are given an identity, various relatively efficient algorithms exist for deciding whether a graph can be switched so that it contains some other graph, the query graph, as an induced subgraph. However, when considering graphs up to isomorphism, we immediately run into the graph isomorphism problem for which no efficient solution is known. Surprisingly enough however, in some cases the decision process can be simplified by transforming the query graph into a "smaller" graph without changing the answer. The main lesson learned is that the size of the query graph is not the dominating factor, but its cycle rank. Although a number of our results hold specifically for undirected, unlabelled graphs, we propose a more general framework and give many positive and negative results for more general cases, where the graphs are labelled with elements of a (finitely generated abelian) group.
This paper discusses new pivoting factorization methods for solving sparse symmetric indefinite systems. As opposed to many existing pivoting methods, our Supernode-Bunch-Kaufman (SBK) pivoting method dynamically sele...
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This paper discusses new pivoting factorization methods for solving sparse symmetric indefinite systems. As opposed to many existing pivoting methods, our Supernode-Bunch-Kaufman (SBK) pivoting method dynamically selects 1 x 1 and 2 x 2 pivots and may be supplemented by pivot perturbation techniques. We demonstrate the effectiveness and the numerical accuracy of this algorithm and also show that a high performance implementation is feasible. We will also show that symmetric maximum-weighted matching strategies add an additional level of reliability to SBK. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques during the numerical factorization. Numerical experiments validate these conclusions.
For a given graph G=(V, E), the interval completion problem of G is to find an edge set F such that the supergraph H =(V, E boolean OR F) of G is an interval graph and vertical bar F vertical bar is minimum. It has be...
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For a given graph G=(V, E), the interval completion problem of G is to find an edge set F such that the supergraph H =(V, E boolean OR F) of G is an interval graph and vertical bar F vertical bar is minimum. It has been shown that it is equivalent to the minimum sum cut problem, the profile minimization problem and a kind of graph searching problems. Furthermore, it has applications in computational biology, archaeology, and clone fingerprinting. In this paper, we show that it is NP-complete on split graphs and propose an efficient algorithm on primitive starlike graphs. (c) 2005 Elsevier B.V. All rights reserved.
Data fusion and multicue data matching are fundamental tasks of high-dimensional data analysis. In this paper, we apply the recently introduced diffusion framework to address these tasks. Our contribution is three-fol...
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Data fusion and multicue data matching are fundamental tasks of high-dimensional data analysis. In this paper, we apply the recently introduced diffusion framework to address these tasks. Our contribution is three-fold: First, we present the Laplace-Beltrami approach for computing density invariant embeddings which are essential for integrating different sources of data. Second, we describe a refinement of the Nystrom extension algorithm called "geometric harmonics." We also explain how to use this tool for data assimilation. Finally, we introduce a multicue data matching scheme based on nonlinear spectral graphs alignment. The effectiveness of the presented schemes is validated by applying it to the problems of lipreading and image sequence alignment.
Given a directed network with two integer weights, cost and delay, associated with each link, Quality-of-Service (QoS) routing requires the determination of a minimum cost path from one node to another node such that ...
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Given a directed network with two integer weights, cost and delay, associated with each link, Quality-of-Service (QoS) routing requires the determination of a minimum cost path from one node to another node such that the delay of the path is bounded by a specified integer value. This problem, also known as the Constrained Shortest Path problem (CSP), admits an Integer Linear Programming (ILP) formulation. Due to the integrality constraints, the problem is NP-hard. So, approximation algorithms have been presented in the literature. Among these, the LARAC algorithm, based on the dual of the LP relaxation of the CSP problem, is very efficient. In contrast to most of the currently available approaches, we study this problem from a primal perspective. Several issues relating to efficient implementations of our approach are discussed. We present two algorithms of pseudopolynomial time complexity. One of these allows degenerate pivots and uses an anticycling strategy and the other, called the NBS algorithm, is based on a novel strategy which avoids degenerate pivots. Experimental results comparing the NBS algorithm, the LARAC algorithm, and general purpose LP solvers are presented. In all cases, the NBS algorithm compares favorably with others and beats them on dense networks.
A set of vertices S subset of V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G - S of the graph, obt...
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A set of vertices S subset of V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G - S of the graph, obtained by making S a clique in the subgraph of G, induced by W U S. We show that such safe separators are a very powerful tool for preprocessing graphs when we want to compute their treewidth. We give several sufficient conditions for separators to be safe, allowing such separators, if existing, to be found in polynomial time. In particular, every inclusion minimal separator of size one or two is safe, every minimum separator of size three that does not split off a component with only one vertex is safe, and every inclusion minimal separator that is an almost clique is safe;an almost clique is a set of vertices W such that there is a u is an element of W with W - {u} a clique. We report on experiments that show significant reductions of instance sizes for graphs from probabilistic networks and frequency assignment. (c) 2006 Elsevier B.V. All rights reserved.
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