1,288 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 tabu search heuristic for the Equitable Coloring Problem
The Equitable Coloring Problem is a variant of the Graph Coloring Problem
where the sizes of two arbitrary color classes differ in at most one unit. This
additional condition, called equity constraints, arises naturally in several
applications. Due to the hardness of the problem, current exact algorithms can
not solve large-sized instances. Such instances must be addressed only via
heuristic methods. In this paper we present a tabu search heuristic for the
Equitable Coloring Problem. This algorithm is an adaptation of the dynamic
TabuCol version of Galinier and Hao. In order to satisfy equity constraints,
new local search criteria are given. Computational experiments are carried out
in order to find the best combination of parameters involved in the dynamic
tenure of the heuristic. Finally, we show the good performance of our heuristic
over known benchmark instances
Squeaky Wheel Optimization
We describe a general approach to optimization which we term `Squeaky Wheel'
Optimization (SWO). In SWO, a greedy algorithm is used to construct a solution
which is then analyzed to find the trouble spots, i.e., those elements, that,
if improved, are likely to improve the objective function score. The results of
the analysis are used to generate new priorities that determine the order in
which the greedy algorithm constructs the next solution. This
Construct/Analyze/Prioritize cycle continues until some limit is reached, or an
acceptable solution is found. SWO can be viewed as operating on two search
spaces: solutions and prioritizations. Successive solutions are only indirectly
related, via the re-prioritization that results from analyzing the prior
solution. Similarly, successive prioritizations are generated by constructing
and analyzing solutions. This `coupled search' has some interesting properties,
which we discuss. We report encouraging experimental results on two domains,
scheduling problems that arise in fiber-optic cable manufacturing, and graph
coloring problems. The fact that these domains are very different supports our
claim that SWO is a general technique for optimization
Algorithms for the minimum sum coloring problem: a review
The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex
coloring problem which has a number of AI related applications. Due to its
theoretical and practical relevance, MSCP attracts increasing attention. The
only existing review on the problem dates back to 2004 and mainly covers the
history of MSCP and theoretical developments on specific graphs. In recent
years, the field has witnessed significant progresses on approximation
algorithms and practical solution algorithms. The purpose of this review is to
provide a comprehensive inspection of the most recent and representative MSCP
algorithms. To be informative, we identify the general framework followed by
practical solution algorithms and the key ingredients that make them
successful. By classifying the main search strategies and putting forward the
critical elements of the reviewed methods, we wish to encourage future
development of more powerful methods and motivate new applications
Reinforcement learning based local search for grouping problems: A case study on graph coloring
Grouping problems aim to partition a set of items into multiple mutually
disjoint subsets according to some specific criterion and constraints. Grouping
problems cover a large class of important combinatorial optimization problems
that are generally computationally difficult. In this paper, we propose a
general solution approach for grouping problems, i.e., reinforcement learning
based local search (RLS), which combines reinforcement learning techniques with
descent-based local search. The viability of the proposed approach is verified
on a well-known representative grouping problem (graph coloring) where a very
simple descent-based coloring algorithm is applied. Experimental studies on
popular DIMACS and COLOR02 benchmark graphs indicate that RLS achieves
competitive performances compared to a number of well-known coloring
algorithms
The Difficulty of Approximating the Chromatic Number for Random Composite Graphs
Combinatorial Optimization is an important class of techniques for solving Combinatorial Problems. Many practical problems are Combinatorial Problems, such as the Traveling Salesman Problem (TSP) and Composite Graph Coloring Problem (CGCP). Unfortunately, both of these problems are NP-complete and it is not known if efficient algorithms exist to solve these problems. Even approximation with guaranteed results can be just as difficult. Recently, many generalized search techniques have been developed to improve upon the solutions found by the heuristic algorithms.
This paper presents results for CGCP. In particular, exact and heuristic algorithms are presented and analyzed. This study is made, to show empirically that CGCP cannot provide guarantees on the approximation using these heuristic methods. In addition, an improvement is presented on the interchange method by Clementson and Elphick that is used with vertex sequential algorithms. This improvement allows graphs of up to 1000 vertices to be colored in considerably less time than previous studies. The study also shows that CDSaturl heuristic does not compete as well with CDSatur as expected for large graphs with edge density of 0.2.
Several NP-completeness theorems are presented and proved. Approximation of CGCP is shown to be as difficult as finding exact solutions if we expect the approximate solutions to fall within a specified bound. These bounds on approximate solutions are shown to be directly related to the bounds that have been proved to exist for the Standard Graph Coloring Problem (SGCP).
Finally, a model of CGCP is developed so that the Tabu Search technique can be applied. Several neighborhoods are developed and tested on 50 and 100 vertex graphs. Timing and performance is analyzed against the heuristics in the previous study. Instances of larger order graphs are used to test the best neighborhood searches with Tabu Search
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