21,116 research outputs found
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
Composing dynamic programming tree-decomposition-based algorithms
Given two integers and as well as graph classes
, the problems
,
, and
ask, given graph
as input, whether , , respectively can be partitioned
into sets such that, for each between and
, , , respectively. Moreover in , we request that the number of edges with
endpoints in different sets of the partition is bounded by . We show that if
there exist dynamic programming tree-decomposition-based algorithms for
recognizing the graph classes , for each , then we can
constructively create a dynamic programming tree-decomposition-based algorithms
for ,
, and
. We show that, in
some known cases, the obtained running times are comparable to those of the
best know algorithms
- β¦