In this article we propose a new single-source shortest-path algorithm that achieves the same O(n center dot m) time bound as the Bellman-Ford-Moore algorithm but outperforms it and other state-of-the-art algorithms i...
详细信息
In this article we propose a new single-source shortest-path algorithm that achieves the same O(n center dot m) time bound as the Bellman-Ford-Moore algorithm but outperforms it and other state-of-the-art algorithms in many cases in practice. Our claims are supported by experimental evidence.
Let G = (V,E) be a graph. We associate with each edge e(i) is an element of E an ordered pair of rational numbers (a(i), b(i)). Let the weight of a spanning tree T, w(T), be defined as Sigma(ei is an element of T) a(i...
详细信息
Let G = (V,E) be a graph. We associate with each edge e(i) is an element of E an ordered pair of rational numbers (a(i), b(i)). Let the weight of a spanning tree T, w(T), be defined as Sigma(ei is an element of T) a(i) + Pi(ei is an element of T) b(i). A spanning tree T in G is called a w-optimum spanning tree if w(T) greater than or equal to w(T') for all spanning trees T' in G. The function w is one instance in a class of two-parameter objectives. Hassin and Tamir proposed a unified approach for solving the class of two-parameter objective optimum spanning tree problems. Let s be an objective in the class and F-s(G) denote the weight of the s-optimum spanning tree of G. The element perturbation problem of the s-optimum spanning tree is to compute F-s(G - e(k)) for all e(k) is an element of E. With Hassin and Tamir's approach, let t(s)(p, q) be the complexity of computing the s-optimum spanning tree where p = \V\ and q = \E\. In this paper, we present an approach to solve the element perturbation problem of the s-optimum spanning tree in t(s)(p, q).
The minimal cost-reliability ratio spanning tree problem is to find a spanning tree such that the cost-reliability ratio is minimized. This problem can also be treated as a specific version of a more generalized probl...
详细信息
The minimal cost-reliability ratio spanning tree problem is to find a spanning tree such that the cost-reliability ratio is minimized. This problem can also be treated as a specific version of a more generalized problem discussed by Hassin and Tamir. By Hassin and Tamir's approach, the minimal cost-reliability ratio spanning tree problem can be solved in O(q(4)) where q is the number of edges in the graph. In this paper, we reduce the complexity of the algorithm proposed by Hassin and Tamir to O(q(3)). Furthermore using our approach, related algorithms proposed by Hassin and Tamir can also be improved by a factor of O(q).
We give a linear-time algorithm to find a feasible flow in a strongly connected network with fixed supplies and demands, each summing to a common value that is at most the minimum arc capacity. This algorithm speeds u...
详细信息
We give a linear-time algorithm to find a feasible flow in a strongly connected network with fixed supplies and demands, each summing to a common value that is at most the minimum arc capacity. This algorithm speeds up the Goldberg-Rao maximum flow method by a constant factor. (C) 2008 Elsevier B.V. All rights reserved.
We present a Theta(log(2) M)-time algorithm that determines an unknown rational number x in Q(M) = {p/q: p, q is an element of{1, . . . , M}} by asking at most 2log(2) M + O(1) queries of the form "Is x less than...
详细信息
We present a Theta(log(2) M)-time algorithm that determines an unknown rational number x in Q(M) = {p/q: p, q is an element of{1, . . . , M}} by asking at most 2log(2) M + O(1) queries of the form "Is x less than or equal to y?". (C) 2002 Elsevier Science B.V. All rights reserved.
In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its pr...
详细信息
In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al. [29] SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.
The effectiveness of a distributed system hinges on the manner in which tasks and data are assigned to the underlying system resources. Moreover, today's large-scale distributed systems must accommodate heterogene...
详细信息
The effectiveness of a distributed system hinges on the manner in which tasks and data are assigned to the underlying system resources. Moreover, today's large-scale distributed systems must accommodate heterogeneity in both the offered load and in the makeup of the available storage and compute capacity. The ideal resource assignment must balance the utilization of the underlying system against the loss of locality incurred when individual tasks or data objects are fragmented among several servers. In this paper we describe this locality-maximizing placement problem and show that an optimal solution is NP-hard. We then describe a polynomial-time algorithm that generates a placement within an additive constant of two from optimal. (C) 2006 Elsevier Inc. All rights reserved.
A new shift operation on nodes of k-ary trees which preserves preorder node numbers is introduced. The shift graph SG(n,k) has as vertices all n-node k-ary trees and edges corresponding to one shift. The graph is prov...
详细信息
A new shift operation on nodes of k-ary trees which preserves preorder node numbers is introduced. The shift graph SG(n,k) has as vertices all n-node k-ary trees and edges corresponding to one shift. The graph is proven to have a Hamiltonian path and an algorithm is presented which generates all n-node k-ary trees successively with constant time between them. (C) 1998 Elsevier Science B.V.
It is well known that the treewidth of a graph G corresponds to the node search number where a team of searchers is pursuing a fugitive that is lazy and invisible (or alternatively is agile and visible) and has the ab...
详细信息
It is well known that the treewidth of a graph G corresponds to the node search number where a team of searchers is pursuing a fugitive that is lazy and invisible (or alternatively is agile and visible) and has the ability to move with infinite speed via unguarded paths. Recently, monotone and connected node search strategies have been considered. A search strategy is monotone if it prevents the fugitive from pervading again areas from where he had been expelled and is connected if, at each step, the set of vertices that is or has been occupied by the searchers induces a connected subgraph of G. It has been shown that the corresponding connected and monotone search number of a graph G can be expressed as the connected treewidth, denoted by ctw(G), that is defined as the minimum width of a rooted tree-decomposition (X, T, r), where the union of the bags corresponding to the nodes of a path of T containing the root r is connected in G. In this paper, we initiate the algorithmic study of connected treewidth. We design a O(n2 center dot log n)-time dynamic programming algorithm to compute the connected treewidth of biconnected series-parallel graphs. At the price of an extra n factor in the running time, our algorithm generalizes to graphs of treewidth at most two.(c) 2021 Elsevier B.V. All rights reserved.
We survey approximation algorithms for some well-known and very natural combinatorial optimization problems, the minimum set covering, the minimum vertex covering, the maximum set packing, and maximum independent set ...
详细信息
We survey approximation algorithms for some well-known and very natural combinatorial optimization problems, the minimum set covering, the minimum vertex covering, the maximum set packing, and maximum independent set problems;we discuss their approximation performance and their complexity. For already known results, any time we have conceived simpler proofs than those already published, we give these proofs, and, for the rest, we cite the simpler published ones. Finally, we discuss how one can relate the approximability behavior (from both a positive and a negative point of view) of vertex covering to the approximability behavior of a restricted class of independent set problems.
暂无评论