Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

Parallelizing RRT on large-scale distributed-memory architectures

This paper addresses the problem of parallelizing the Rapidly-exploring Random Tree (RRT) algorithm on large-scale distributed-memory architectures, using the Message Passing Interface. We compare three parallel versions of RRT based on classical parallelization schemes. We evaluate them on different motion planning problems and analyze the various factors influencing their performance

Parallelizing RRT on distributed-memory architectures

This paper addresses the problem of improving the performance of the Rapidly-exploring Random Tree (RRT) algorithm by parallelizing it. For scalability reasons we do so on a distributed-memory architecture, using the message-passing paradigm. We present three parallel versions of RRT along with the technicalities involved in their implementation. We also evaluate the algorithms and study how they behave on different motion planning problems