5 research outputs found
An analysis between exact and approximate algorithms for the k-center problem in graphs
This research focuses on the k-center problem and its applications. Different methods for solving this problem are analyzed. The implementations of an exact algorithm and of an approximate algorithm are presented. The source code and the computation complexity of these algorithms are presented and analyzed. The multitasking mode of the operating system is taken into account considering the execution time of the algorithms. The results show that the approximate algorithm finds solutions that are not worse than two times optimal. In some case these solutions are very close to the optimal solutions, but this is true only for graphs with a smaller number of nodes. As the number of nodes in the graph increases (respectively the number of edges increases), the approximate solutions deviate from the optimal ones, but remain acceptable. These results give reason to conclude that for graphs with a small number of nodes the approximate algorithm finds comparable solutions with those founds by the exact algorithm
Matroid and Knapsack Center Problems
In the classic -center problem, we are given a metric graph, and the
objective is to open nodes as centers such that the maximum distance from
any vertex to its closest center is minimized. In this paper, we consider two
important generalizations of -center, the matroid center problem and the
knapsack center problem. Both problems are motivated by recent content
distribution network applications. Our contributions can be summarized as
follows:
1. We consider the matroid center problem in which the centers are required
to form an independent set of a given matroid. We show this problem is NP-hard
even on a line. We present a 3-approximation algorithm for the problem on
general metrics. We also consider the outlier version of the problem where a
given number of vertices can be excluded as the outliers from the solution. We
present a 7-approximation for the outlier version.
2. We consider the (multi-)knapsack center problem in which the centers are
required to satisfy one (or more) knapsack constraint(s). It is known that the
knapsack center problem with a single knapsack constraint admits a
3-approximation. However, when there are at least two knapsack constraints, we
show this problem is not approximable at all. To complement the hardness
result, we present a polynomial time algorithm that gives a 3-approximate
solution such that one knapsack constraint is satisfied and the others may be
violated by at most a factor of . We also obtain a 3-approximation
for the outlier version that may violate the knapsack constraint by
.Comment: A preliminary version of this paper is accepted to IPCO 201
Fault-Tolerant Hotelling Games
The -player Hotelling game calls for each player to choose a point on the
line segment, so as to maximize the size of his Voronoi cell. This paper
studies fault-tolerant versions of the Hotelling game. Two fault models are
studied: line faults and player faults. The first model assumes that the
environment is prone to failure: with some probability, a disconnection occurs
at a random point on the line, splitting it into two separate segments and
modifying each player's Voronoi cell accordingly. A complete characterization
of the Nash equilibria of this variant is provided for every . Additionally,
a one to one correspondence is shown between equilibria of this variant and of
the Hotelling game with no faults. The second fault model assumes the players
are prone to failure: each player is removed from the game with i.i.d.
probability, changing the payoffs of the remaining players accordingly. It is
shown that for this variant of the game has no Nash equilibria