21,568 research outputs found
Heuristic algorithms for the min-max edge 2-coloring problem
In multi-channel Wireless Mesh Networks (WMN), each node is able to use
multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004,
INFOCOM 2005) propose and study several such architectures in which a computer
can have multiple network interface cards. These architectures are modeled as a
graph problem named \emph{maximum edge -coloring} and studied in several
papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016).
Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an
alternative variant, named the \emph{min-max edge -coloring}.
The above mentioned graph problems, namely the maximum edge -coloring and
the min-max edge -coloring are studied mainly from the theoretical
perspective. In this paper, we study the min-max edge 2-coloring problem from a
practical perspective. More precisely, we introduce, implement and test four
heuristic approximation algorithms for the min-max edge -coloring problem.
These algorithms are based on a \emph{Breadth First Search} (BFS)-based
heuristic and on \emph{local search} methods like basic \emph{hill climbing},
\emph{simulated annealing} and \emph{tabu search} techniques, respectively.
Although several algorithms for particular graph classes were proposed by
Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques,
hypergraphs), we design the first algorithms for general graphs.
We study and compare the running data for all algorithms on Unit Disk Graphs,
as well as some graphs from the DIMACS vertex coloring benchmark dataset.Comment: This is a post-peer-review, pre-copyedit version of an article
published in International Computing and Combinatorics Conference
(COCOON'18). The final authenticated version is available online at:
http://www.doi.org/10.1007/978-3-319-94776-1_5
A genetic algorithm for the partial binary constraint satisfaction problem: an application to a frequency assignment problem
We describe a genetic algorithm for the partial constraint satisfaction problem. The typical elements of a genetic algorithm, selection, mutation and cross-over, are filled in with combinatorial ideas. For instance, cross-over of two solutions is performed by taking the one or two domain elements in the solutions of each of the variables as the complete domain of the variable. Then a branch-and-bound method is used for solving this small instance. When tested on a class of frequency assignment problems this genetic algorithm produced the best known solutions for all test problems. This feeds the idea that combinatorial ideas may well be useful in genetic algorithms.Economics ;
Decentralized Constraint Satisfaction
We show that several important resource allocation problems in wireless
networks fit within the common framework of Constraint Satisfaction Problems
(CSPs). Inspired by the requirements of these applications, where variables are
located at distinct network devices that may not be able to communicate but may
interfere, we define natural criteria that a CSP solver must possess in order
to be practical. We term these algorithms decentralized CSP solvers. The best
known CSP solvers were designed for centralized problems and do not meet these
criteria. We introduce a stochastic decentralized CSP solver and prove that it
will find a solution in almost surely finite time, should one exist, also
showing it has many practically desirable properties. We benchmark the
algorithm's performance on a well-studied class of CSPs, random k-SAT,
illustrating that the time the algorithm takes to find a satisfying assignment
is competitive with stochastic centralized solvers on problems with order a
thousand variables despite its decentralized nature. We demonstrate the
solver's practical utility for the problems that motivated its introduction by
using it to find a non-interfering channel allocation for a network formed from
data from downtown Manhattan
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