20,252 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
The min-max edge q-coloring problem
In this paper we introduce and study a new problem named \emph{min-max edge
-coloring} which is motivated by applications in wireless mesh networks. The
input of the problem consists of an undirected graph and an integer . The
goal is to color the edges of the graph with as many colors as possible such
that: (a) any vertex is incident to at most different colors, and (b) the
maximum size of a color group (i.e. set of edges identically colored) is
minimized. We show the following results: 1. Min-max edge -coloring is
NP-hard, for any . 2. A polynomial time exact algorithm for min-max
edge -coloring on trees. 3. Exact formulas of the optimal solution for
cliques and almost tight bounds for bicliques and hypergraphs. 4. A non-trivial
lower bound of the optimal solution with respect to the average degree of the
graph. 5. An approximation algorithm for planar graphs.Comment: 16 pages, 5 figure
Dichotomies properties on computational complexity of S-packing coloring problems
This work establishes the complexity class of several instances of the
S-packing coloring problem: for a graph G, a positive integer k and a non
decreasing list of integers S = (s\_1 , ..., s\_k ), G is S-colorable, if its
vertices can be partitioned into sets S\_i , i = 1,... , k, where each S\_i
being a s\_i -packing (a set of vertices at pairwise distance greater than
s\_i). For a list of three integers, a dichotomy between NP-complete problems
and polynomial time solvable problems is determined for subcubic graphs.
Moreover, for an unfixed size of list, the complexity of the S-packing coloring
problem is determined for several instances of the problem. These properties
are used in order to prove a dichotomy between NP-complete problems and
polynomial time solvable problems for lists of at most four integers
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
Algorithms for Fast Aggregated Convergecast in Sensor Networks
Fast and periodic collection of aggregated data
is of considerable interest for mission-critical and continuous
monitoring applications in sensor networks. In the many-to-one
communication paradigm, referred to as convergecast, we focus
on applications wherein data packets are aggregated at each hop
en-route to the sink along a tree-based routing topology, and
address the problem of minimizing the convergecast schedule
length by utilizing multiple frequency channels. The primary
hindrance in minimizing the schedule length is the presence of
interfering links. We prove that it is NP-complete to determine
whether all the interfering links in an arbitrary network can
be removed using at most a constant number of frequencies.
We give a sufficient condition on the number of frequencies for
which all the interfering links can be removed, and propose a
polynomial time algorithm that minimizes the schedule length
in this case. We also prove that minimizing the schedule length
for a given number of frequencies on an arbitrary network is
NP-complete, and describe a greedy scheme that gives a constant
factor approximation on unit disk graphs. When the routing tree
is not given as an input to the problem, we prove that a constant
factor approximation is still achievable for degree-bounded trees.
Finally, we evaluate our algorithms through simulations and
compare their performance under different network parameters
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