Eppstein [5] characterized the minor-closed graph families for which the treewidth is bounded by a function of the diameter, which includes, e.g., planar graphs. This characterization has been used as the basis for se...
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Eppstein [5] characterized the minor-closed graph families for which the treewidth is bounded by a function of the diameter, which includes, e.g., planar graphs. This characterization has been used as the basis for several (approximation) algorithms on such graphs (e.g., [2] and [5]-[8]). The proof of Eppstein is complicated. In this short paper we obtain the same characterization with a simple proof. In addition, the relation between treewidth and diameter is slightly better and explicit.
The average distance of a connected graph G is the average of the distances between all pairs of vertices of G. We present a linear time algorithm that determines, for a given interval graph G, a spanning tree of G wi...
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The average distance of a connected graph G is the average of the distances between all pairs of vertices of G. We present a linear time algorithm that determines, for a given interval graph G, a spanning tree of G with minimum average distance (MAD tree). Such a tree is sometimes referred to as a minimum routing cost spanning tree. (C) 2003 Elsevier B.V. All rights reserved.
In this paper, we give an algorithm for the node-to-set disjoint paths problem in transposition graphs. The algorithm is of polynomial order of n for an n-transposition graph. It is based on recursion and divided into...
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ISBN:
(纸本)1932415262
In this paper, we give an algorithm for the node-to-set disjoint paths problem in transposition graphs. The algorithm is of polynomial order of n for an n-transposition graph. It is based on recursion and divided into two cases according to the distribution of destination nodes. The maximum length of each path and the time complexity of the algorithm are estimated and the average performance is evaluated based on computer experiment.
Given a 2-node connected, real weighted, and undirected graph G=(V,E), with n nodes and m edges, and given a minimum spanning tree (MST) T=(V,E-T) of G, we study the problem of finding, for every node upsilon is an el...
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Given a 2-node connected, real weighted, and undirected graph G=(V,E), with n nodes and m edges, and given a minimum spanning tree (MST) T=(V,E-T) of G, we study the problem of finding, for every node upsilon is an element of V, a set of replacement edges which can be used for constructing an MST of G-upsilon (i.e., the graph G deprived of upsilon and all its incident edges). We show that this problem can be solved on a pointer machine in O(***(m,n)) time and O.(m) space, where alpha is the functional inverse of Ackermann's function. Our solution improves over the previously best known O(min{***(n,n), m + n log n}) time bound, and allows us to close the gap existing with the fastest solution for the edge-removal version of the problem (i.e., that of finding, for every edge e is an element ofE(T), a replacement edge which can be used for constructing an MST of G-e=(V,E\{e})). Our algorithm finds immediate application in maintaining MST-based communication networks undergoing temporary node failures. Moreover, in a distributed environment in which nodes are managed by selfish agents, it can be used to design an efficient, truthful mechanism for building an MST.
MATRIX DOMINATION is the NP-complete problem of determining whether a given {0,1} matrix contains a set of k non-zero entries that are in the same row or same column as all other non-zero entries. Using a kernelizatio...
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MATRIX DOMINATION is the NP-complete problem of determining whether a given {0,1} matrix contains a set of k non-zero entries that are in the same row or same column as all other non-zero entries. Using a kernelization and search tree approach, we show the problem to be fixed-parameter tractable with running time O(n(3) + 1.959(k) k(5/2)). (C) 2004 Elsevier B.V. All rights reserved.
We study universal stability of directed and undirected graphs in the adversarial queuing model for static packet routing. In this setting, packets are injected in some edge and have to traverse a predefined path befo...
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We study universal stability of directed and undirected graphs in the adversarial queuing model for static packet routing. In this setting, packets are injected in some edge and have to traverse a predefined path before leaving the system. Restrictions on the allowed packet trajectory provide a way to analyze stability under different packet trajectories. We consider five packet trajectories, two for directed graphs and three for undirected graphs, and provide polynomial time algorithms for testing universal stability when considering each of them. In each case we obtain a different characterization of the universal stability property in terms of a set of forbidden subgraphs. Thus we show that variations of the allowed packet trajectory lead to nonequivalent characterizations. Using those characterizations we are also able to provide polynomial time algorithms for testing stability under the NTG-lis (Nearest To Go-Longest In System) protocol.
After [15], [31], [19], [8], [25], [5], minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimiza...
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After [15], [31], [19], [8], [25], [5], minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/maxflow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push-relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.
We consider ad hoc wireless networks that are configured as Mobile Backbone Networks. A hierarchical network architecture is synthesized, consisting of Access Nets (ANets) and Backbone Nets (BNets). Each ANet is manag...
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We consider ad hoc wireless networks that are configured as Mobile Backbone Networks. A hierarchical network architecture is synthesized, consisting of Access Nets (ANets) and Backbone Nets (BNets). Each ANet is managed by a (dynamically elected) Backbone Node (BN) that is equipped with higher capability (transmission and processing) modules. The BNs are chosen from currently active mobile backbone-capable nodes or are represented by (ground and/or airborne) unmanned vehicles (UVs) that are guided into selected positions. In this paper, we develop and investigate a new joint power controlled medium access control (MAC) algorithm for wireless access nets (ANets). Under our new protocol, the net backbone node instructs the ANet nodes to make power control adjustments while simultaneously allocating to them slots for the requested transmissions of their packets. This algorithm, in contrast to other employed conventional graph-based scheduling algorithms, satisfies the requirement that a minimum signal-to-interference and noise ratio (SINR) is met at all intended receivers. We show our algorithm to lead to a significant increase in the net throughput level by attaining high spatial reuse.
An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the in...
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An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weight vector represents the number of calls to be assigned at vertices. In this paper we present a 2-local distributed algorithm for multicoloring triangle-free hexagonal graphs using only the local clique numbers omega(1)(v) and omega(2)(v) at each vertex v of the given hexagonal graph, which can be computed from local information available at the vertex. We prove that the algorithm uses no more than [5omega(G)/4] + 3 colors for any triangle-free hexagonal graph G, without explicitly computing the global clique number omega(G). Hence the competitive ratio of the algorithm is 5/4. (C) 2004 Elsevier B.V. All rights reserved.
We motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have poly-logarithmic worst-case ...
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We motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have poly-logarithmic worst-case guarantees under the new measure. The main result of the article is the analysis of a popular spectral algorithm. One variant of spectral clustering turns out to have effective worst-case guarantees;another finds a "good" clustering, if one exists.
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