Results 1  10
of
13
A general approximation technique for constrained forest problems
 in Proceedings of the 3rd Annual ACMSIAM Symposium on Discrete Algorithms
, 1992
"... Abstract. We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimizatio ..."
Abstract

Cited by 355 (21 self)
 Add to MetaCart
Abstract. We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result is obtained for the 2matching problem and its variants. We also derive the first approximation algorithms for many NPcomplete problems, including the nonfixed pointtopoint connection problem, the exact path partitioning problem, and complex locationdesign problems. Moreover, for the prizecollecting traveling salesman or Steiner tree problems, we obtain 2approximation algorithms, therefore improving the previously bestknown performance guarantees of 2.5 and 3, respectively [Math. Programming, 59 (1993), pp. 413420].
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
Abstract

Cited by 123 (7 self)
 Add to MetaCart
The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
On Network Design Problems: Fixed Cost Flows and the Covering Steiner Problem
, 2001
"... Network design problems, such as generalizations of the Steiner Tree Problem, can be cast as edgecostow problems. An edgecost ow problem is a mincost ow problem in which the cost of the ow equals the sum of the costs of the edges carrying positive ow. ..."
Abstract

Cited by 23 (3 self)
 Add to MetaCart
Network design problems, such as generalizations of the Steiner Tree Problem, can be cast as edgecostow problems. An edgecost ow problem is a mincost ow problem in which the cost of the ow equals the sum of the costs of the edges carrying positive ow.
Restricted Delivery Problems on a Network
, 1996
"... We consider a delivery problem on a network one is given a network in which nodes have supplies or demands for certain products, and arcs have lengths satisfying the Triangle Inequality. A vehicle of infinite capacity, travels through the network, carrying products to their destinations, and is limi ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We consider a delivery problem on a network one is given a network in which nodes have supplies or demands for certain products, and arcs have lengths satisfying the Triangle Inequality. A vehicle of infinite capacity, travels through the network, carrying products to their destinations, and is limited in that it can carry only a single type of product at a time. The general problem asks for a shortest delivery route of all products from their origin to their destination. Here we consider certain restrictions on the delivery paths allowed, and compare the quality of the solution of the unrestricted problem to that of the restricted one. Both the general and restricted problems are NPhard, and we discuss approximation algorithms. We also give a constant factor approximation algorithm for the Clustered Traveling Salesman Problem. Keywords: Traveling salesman problem, approximation algorithm. 1 Introduction In this paper we are concerned with a delivery problem on a network. We are gi...
The directed steiner network problem is tractable for a constant number of terminals
 In Proceedings FOCS
, 1999
"... We consider the DIRECTED STEINER NETWORK problem, also called the POINTTOPOINT CONNECTION problem, where given a directed graph G and p pairs s1 t1 sp tp of nodes in the graph, one has to find the smallest subgraph H of G that contains paths from si to ti for all i. The problem is NPhard for gene ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We consider the DIRECTED STEINER NETWORK problem, also called the POINTTOPOINT CONNECTION problem, where given a directed graph G and p pairs s1 t1 sp tp of nodes in the graph, one has to find the smallest subgraph H of G that contains paths from si to ti for all i. The problem is NPhard for general p, since the DIRECTED STEINER TREE problem is a special case. Until now, the complexity was unknown for constant p 3. We prove that the problem is polynomially solvable if p is any constant number, even if nodes and edges in G are weighted and the goal is to minimize the total weight of the subgraph H. In addition, we give an efficient algorithm for the STRONGLY CONNECTED STEINER SUBGRAPH problem for any constant p, where given a directed graph and p nodes in the graph, one has to compute the smallest strongly connected subgraph containing the p nodes.
Asynchronous Organizations for Solving the PointtoPoint Connection Problem
, 1998
"... We present an agent approach to solve the nonfixed pointtopoint connection problem. The optimization version of this problem is NPhard and has numerous applications in circuit switching and VLSI design. We use Asynchronous Teams (or ATeams) technique to search for an optimal global solution. An ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
We present an agent approach to solve the nonfixed pointtopoint connection problem. The optimization version of this problem is NPhard and has numerous applications in circuit switching and VLSI design. We use Asynchronous Teams (or ATeams) technique to search for an optimal global solution. An ATeam is an organization of agents that communicate with each other by means of shared memories. Each agent is a heuristic strategy that can make its own choices about its inputs, scheduling and resource allocation. Computational results comparing our approach with an exact algorithm proposed by Meneses are presented.
A parallel Implementation of an Asynchronous Team to the Pointtopoint Connection Problem
, 2003
"... We propose a parallel and asynchronous approach to give nearoptimal solutions to the nonfixed pointtopoint connection problem. This problem is NPhard and has practical applications in multicast routing. The technique adopted to solve the problem is an organization of heuristics that communicate ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We propose a parallel and asynchronous approach to give nearoptimal solutions to the nonfixed pointtopoint connection problem. This problem is NPhard and has practical applications in multicast routing. The technique adopted to solve the problem is an organization of heuristics that communicate with each other by means of a virtually shared memory.
Escaping a grid by edgedisjoint paths
 In Proc. of the eleventh annual ACMSIAM symposium on Discrete algorithms
, 2000
"... We study the edgedisjoint escape problem in grids. Given a set of n sources in a twodimensional grid, the problem is to connect all sources to the grid boundary using a set of n edgedisjoint paths. Different from the conventional approach, which reduces the problem to a network flow problem, we s ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We study the edgedisjoint escape problem in grids. Given a set of n sources in a twodimensional grid, the problem is to connect all sources to the grid boundary using a set of n edgedisjoint paths. Different from the conventional approach, which reduces the problem to a network flow problem, we solve the problem by first ensuring that no rectangle in the grid contain more sources than outlets, a necessary and sufficient condition for the existence of a solution. Based on this condition, we give a greedy algorithm that finds the paths in O(n 2) time, which is faster than all previous approaches. This problem finds applications in pointtopoint delivery, VLSI reconfiguration, and package routing. 1
Steiner Trees and Beyond: Approximation Algorithms for Network Design
, 1993
"... We present approximation algorithms for several NPhard optimization problems arising in network design. Almost all of our algorithms run in polynomial time and output solutions with a worstcase performance guarantee on the quality of the output solution. A typical problem that we consider can be s ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We present approximation algorithms for several NPhard optimization problems arising in network design. Almost all of our algorithms run in polynomial time and output solutions with a worstcase performance guarantee on the quality of the output solution. A typical problem that we consider can be stated as follows: given an undirected graph and certain connectivity requirements, find a subgraph that satisfies these requirements and has minimum cost. In this thesis, we address many different connectivity requirements such as spanning trees, Steiner trees, generalized Steiner forests, and twoconnected networks. The cost criteria that we consider range from the total cost of the edges in the network, the total cost of the nodes in the network, the maximum degree of any node in the network, the maximum cost of any edge in the network to some combination of these. We also address the maximumleaf spanning tree problem and provide the first approximation algorithms for this problem. In t...
A BranchandCut to the PointtoPoint Connection Problem on Multicast Networks
"... In multicast routing, one of the basic problems consists of sending data from a set of sources to a set of destinations with minimum cost. A formalization of this problem using graph theory is given by the nonfixed PointtoPoint Connection (PPC) Problem. The optimization version of this problem is ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
In multicast routing, one of the basic problems consists of sending data from a set of sources to a set of destinations with minimum cost. A formalization of this problem using graph theory is given by the nonfixed PointtoPoint Connection (PPC) Problem. The optimization version of this problem is known to be NPhard, and it can be also applied in areas such as circuit switching and VLSI design. We present a branchandcut approach to solve the PPC. Initially we describe a 01 integer programming formulation. Then, we prove that some of the constraints in this formulation are facet defining inequalities. Other valid inequalities, based on partitions of the set of vertices in the graph are also investigated. The proposed branchandcut algorithm is based on the previously discussed inequalities. Computational results of the branchandcut algorithm are presented, with comparisons to existing heuristic and approximation algorithms. The results show the e#ectiveness of the branchandcut method for instances of moderate size.