Results 11  20
of
27
Random PseudoPolynomial Algorithms for Exact Matroid Problems
, 1992
"... In this work we present a random pseudopolynomial algorithm for the problem of finding a base of specified value in a weighted represented matroid, subject to parity conditions. We also describe a specialized version of the algorithm suitable for finding a base of specified value in the intersectio ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
In this work we present a random pseudopolynomial algorithm for the problem of finding a base of specified value in a weighted represented matroid, subject to parity conditions. We also describe a specialized version of the algorithm suitable for finding a base of specified value in the intersection of two matroids. This result generalizes an existing pseudopolynomial algorithm for computing exact arborescences in weighted graphs. Another (simpler) specialized version of our algorithms is also presented for computing perfect matchings of specified value in weighted graphs.
Automated Discovery of Active Motifs in Three Dimensional Molecules
 In Proceedings of the 3rd International Conference on Knowledge Discovery and Data Mining
, 1997
"... In this paper we present a method for discovering approximately common motifs (also known as active motifs) in three dimensional (3D) molecules. Each node in a molecule is represented by a 3D point in the Euclidean Space and each edge is represented by an undirected line segment connecting two ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
In this paper we present a method for discovering approximately common motifs (also known as active motifs) in three dimensional (3D) molecules. Each node in a molecule is represented by a 3D point in the Euclidean Space and each edge is represented by an undirected line segment connecting two nodes in the molecule. Motifs are rigid substructures which may occur in a molecule after allowing for an arbitrary number of rotations and translations as well as a small number (specified by the user) of node insert/delete operations in the motifs or the molecule. (We call this "approximate occurrence.") The proposed method combines the geometric hashing technique and block detection algorithms for undirected graphs. To demonstrate the utility of our algorithms, we discuss their applications to classifying three families of molecules pertaining to antibacterial sulfa drugs, antianxiety agents (benzodiazepines) and antiadrenergic agents (fi receptors). Experimental results i...
RNCApproximation Algorithms for the Steiner Problem
 Proc. STACS'97
, 1997
"... . In this paper we present an RNCalgorithm for finding a minimum spanning tree in a weighted 3uniform hypergraph, assuming the edge weights are given in unary, and a fully polynomial time randomized approximation scheme if the edge weights are given in binary. From this result we then derive RNCa ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
. In this paper we present an RNCalgorithm for finding a minimum spanning tree in a weighted 3uniform hypergraph, assuming the edge weights are given in unary, and a fully polynomial time randomized approximation scheme if the edge weights are given in binary. From this result we then derive RNCapproximation algorithms for the Steiner problem in networks with approximation ratio (1 + ffl) 5=3 for all ffl ? 0. 1 Introduction In recent years, the Steiner tree problem in graphs attracted considerable attention, as well from the theoretical point of view as from its applicability, e.g., in VLSIlayout. It is rather easy to see and has been known for a long time that a minimum Steiner tree spanning a given set of terminals in a graph or network can be approximated in polynomial time up to a factor of 2, cf. e.g. Choukhmane [6] or Kou, Markowsky, Berman [14]. After a long period without any progress Zelikovsky [23], Berman and Ramaiyer [2], Zelikovsky [24], and Karpinski and Zelikovsky ...
A lineartime approximation algorithm for weighted matchings in graphs
 ACM TRANSACTIONS ON ALGORITHMS
, 2005
"... Approximation algorithms have so far mainly been studied for problems that are not known to have polynomial time algorithms for solving them exactly. Here we propose an approximation algorithm for the weighted matching problem in graphs which can be solved in polynomial time. The weighted matching p ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
Approximation algorithms have so far mainly been studied for problems that are not known to have polynomial time algorithms for solving them exactly. Here we propose an approximation algorithm for the weighted matching problem in graphs which can be solved in polynomial time. The weighted matching problem is to find a matching in an edge weighted graph that has maximum weight. The first polynomialtime algorithm for this problem was given by Edmonds in 1965. The fastest known algorithm for the weighted matching problem has a running time of O(nm + n² log n). Many real world problems require graphs of such large size that this running time is too costly. Therefore, there is considerable need for faster approximation algorithms for the weighted matching problem. We present a lineartime approximation algorithm for the weighted matching problem with a performance ratio arbitrarily close to 2/1. This improves the previously best performance ratio of 3/2. Our algorithm is not only of theoretical interest, but because it is easy to implement and the constants involved are quite small it is also useful in practice.
A LargeGrain Parallel Sparse System Solver
 In Proc. Fourth SIAM Conf. on Parallel Proc. for Scient. Comp
, 1989
"... . The efficiency of solving sparse linear systems on parallel processors and more complex multicluster architectures such as Cedar is greatly enhanced if relatively large grain computational tasks can be assigned to each cluster or processor. The ordering of a system into a bordered block upper tria ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
. The efficiency of solving sparse linear systems on parallel processors and more complex multicluster architectures such as Cedar is greatly enhanced if relatively large grain computational tasks can be assigned to each cluster or processor. The ordering of a system into a bordered block upper triangular form facilitates a reasonable largegrain partitioning. A new algorithm which produces this form for unsymmetric sparse linear systems is considered and the associated factorization algorithm is presented. Computational results are presented for the Cedar multiprocessor. Several techniques have been proposed to solve large sparse systems of linear equations on parallel processors. A key task which determines the effectiveness of these techniques is the identification and exploitation of the computational granularity appropriate for the target multiprocessor architecture. Many algorithms assume special properties such as symmetric positive definiteness or exploit knowledge of the appl...
A scaling algorithm for maximum weight matching in bipartite graphs
 IN: PROCEEDINGS 23RD ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
"... Given a weighted bipartite graph, the maximum weight matching (MWM) problem is to find a set of vertexdisjoint edges with maximum weight. We present a new scaling algorithm that runs in O(m √ n log N) time, when the weights are integers within the range of [0, N]. The result improves the previous b ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Given a weighted bipartite graph, the maximum weight matching (MWM) problem is to find a set of vertexdisjoint edges with maximum weight. We present a new scaling algorithm that runs in O(m √ n log N) time, when the weights are integers within the range of [0, N]. The result improves the previous bounds of O(Nm √ n) by Gabow and O(m √ n log (nN)) by Gabow and Tarjan over 20 years ago. Our improvement draws ideas from a not widely known result, the primal method by Balinski and Gomory.
Incremental assignment problem
 Information Sciences
, 2007
"... In this paper we introduce the incremental assignment problem. In this problem, a new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum weighted matching is already known, and the maximum weighted matching of the extended graph is sought. We propose an O ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
In this paper we introduce the incremental assignment problem. In this problem, a new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum weighted matching is already known, and the maximum weighted matching of the extended graph is sought. We propose an O(V  2) algorithm for the problem.
An additive branchandbound algorithm for the pickup and delivery traveling salesman problem with lifo loading. submitted
"... This paper introduces an additive branchandbound algorithm for two variants of the pickup and delivery traveling salesman problem in which loading and unloading operations have to be performed either in a LastInFirstOut (LIFO) or in a FirstInFirstOut (FIFO) order. Two relaxations are used wi ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
This paper introduces an additive branchandbound algorithm for two variants of the pickup and delivery traveling salesman problem in which loading and unloading operations have to be performed either in a LastInFirstOut (LIFO) or in a FirstInFirstOut (FIFO) order. Two relaxations are used within the additive approach: the assignment problem and the shortest spanning rarborescence problem. The quality of the lower bounds is further improved by a set of elimination rules applied at each node of the search tree to remove from the problem arcs that cannot belong to feasible solutions because of precedence relationships. The performance of the algorithm and the effectiveness of the elimination rules are assessed on instances from the literature.
Scaling algorithms for approximate and exact maximum weight matching
, 2011
"... The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the following sense. For any ɛ> 0, we give an algorithm that computes a (1 − ɛ)approximate maximum weight matching in O(mɛ −1 log ɛ −1) time, that is, optimal linear time for any fixed ɛ. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error. Our second contribution is a new exact maximum weight matching algorithm for integerweighted bipartite graphs that runs in time O(m √ n log N). This improves on the O(Nm √ n)time and O(m √ n log(nN))time algorithms known since the mid 1980s, for 1 ≪ log N ≪ log n. Here N is the maximum integer edge weight. 1