2,502 research outputs found
Parameterized Algorithms for Load Coloring Problem
One way to state the Load Coloring Problem (LCP) is as follows. Let
be graph and let be a 2-coloring. An
edge is called red (blue) if both end-vertices of are red (blue).
For a 2-coloring , let and be the number of red and blue edges
and let . Let be the maximum of
over all 2-colorings.
We introduce the parameterized problem -LCP of deciding whether , where is the parameter. We prove that this problem admits a kernel with
at most . Ahuja et al. (2007) proved that one can find an optimal
2-coloring on trees in polynomial time. We generalize this by showing that an
optimal 2-coloring on graphs with tree decomposition of width can be found
in time . We also show that either is a Yes-instance of -LCP
or the treewidth of is at most . Thus, -LCP can be solved in time
$O^*(4^k).
Parameterized TSP: Beating the Average
In the Travelling Salesman Problem (TSP), we are given a complete graph
together with an integer weighting on the edges of , and we are asked
to find a Hamilton cycle of of minimum weight. Let denote the
average weight of a Hamilton cycle of for the weighting . Vizing
(1973) asked whether there is a polynomial-time algorithm which always finds a
Hamilton cycle of weight at most . He answered this question in the
affirmative and subsequently Rublineckii (1973) and others described several
other TSP heuristics satisfying this property. In this paper, we prove a
considerable generalisation of Vizing's result: for each fixed , we give an
algorithm that decides whether, for any input edge weighting of ,
there is a Hamilton cycle of of weight at most (and constructs
such a cycle if it exists). For fixed, the running time of the algorithm is
polynomial in , where the degree of the polynomial does not depend on
(i.e., the generalised Vizing problem is fixed-parameter tractable with respect
to the parameter )
A Memetic Algorithm for the Generalized Traveling Salesman Problem
The generalized traveling salesman problem (GTSP) is an extension of the
well-known traveling salesman problem. In GTSP, we are given a partition of
cities into groups and we are required to find a minimum length tour that
includes exactly one city from each group. The recent studies on this subject
consider different variations of a memetic algorithm approach to the GTSP. The
aim of this paper is to present a new memetic algorithm for GTSP with a
powerful local search procedure. The experiments show that the proposed
algorithm clearly outperforms all of the known heuristics with respect to both
solution quality and running time. While the other memetic algorithms were
designed only for the symmetric GTSP, our algorithm can solve both symmetric
and asymmetric instances.Comment: 15 pages, to appear in Natural Computing, Springer, available online:
http://www.springerlink.com/content/5v4568l492272865/?p=e1779dd02e4d4cbfa49d0d27b19b929f&pi=1
Constraint Expressions and Workflow Satisfiability
A workflow specification defines a set of steps and the order in which those
steps must be executed. Security requirements and business rules may impose
constraints on which users are permitted to perform those steps. A workflow
specification is said to be satisfiable if there exists an assignment of
authorized users to workflow steps that satisfies all the constraints. An
algorithm for determining whether such an assignment exists is important, both
as a static analysis tool for workflow specifications, and for the construction
of run-time reference monitors for workflow management systems. We develop new
methods for determining workflow satisfiability based on the concept of
constraint expressions, which were introduced recently by Khan and Fong. These
methods are surprising versatile, enabling us to develop algorithms for, and
determine the complexity of, a number of different problems related to workflow
satisfiability.Comment: arXiv admin note: text overlap with arXiv:1205.0852; to appear in
Proceedings of SACMAT 201
Parameterized Study of the Test Cover Problem
We carry out a systematic study of a natural covering problem, used for
identification across several areas, in the realm of parameterized complexity.
In the {\sc Test Cover} problem we are given a set of items
together with a collection, , of distinct subsets of these items called
tests. We assume that is a test cover, i.e., for each pair of items
there is a test in containing exactly one of these items. The
objective is to find a minimum size subcollection of , which is still a
test cover. The generic parameterized version of {\sc Test Cover} is denoted by
-{\sc Test Cover}. Here, we are given and a
positive integer parameter as input and the objective is to decide whether
there is a test cover of size at most . We study four
parameterizations for {\sc Test Cover} and obtain the following:
(a) -{\sc Test Cover}, and -{\sc Test Cover} are fixed-parameter
tractable (FPT).
(b) -{\sc Test Cover} and -{\sc Test Cover} are
W[1]-hard. Thus, it is unlikely that these problems are FPT
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