72 research outputs found
Improvements on the k-center problem for uncertain data
In real applications, there are situations where we need to model some
problems based on uncertain data. This leads us to define an uncertain model
for some classical geometric optimization problems and propose algorithms to
solve them. In this paper, we study the -center problem, for uncertain
input. In our setting, each uncertain point is located independently from
other points in one of several possible locations in a metric space with metric , with specified probabilities
and the goal is to compute -centers that minimize the
following expected cost here
is the probability space of all realizations of given uncertain points and
In restricted assigned version of this problem, an assignment is given for any choice of centers and the
goal is to minimize In unrestricted version, the
assignment is not specified and the goal is to compute centers
and an assignment that minimize the above expected
cost.
We give several improved constant approximation factor algorithms for the
assigned versions of this problem in a Euclidean space and in a general metric
space. Our results significantly improve the results of \cite{guh} and
generalize the results of \cite{wang} to any dimension. Our approach is to
replace a certain center point for each uncertain point and study the
properties of these certain points. The proposed algorithms are efficient and
simple to implement
An optimal algorithm for the weighted backup 2-center problem on a tree
In this paper, we are concerned with the weighted backup 2-center problem on
a tree. The backup 2-center problem is a kind of center facility location
problem, in which one is asked to deploy two facilities, with a given
probability to fail, in a network. Given that the two facilities do not fail
simultaneously, the goal is to find two locations, possibly on edges, that
minimize the expected value of the maximum distance over all vertices to their
closest functioning facility. In the weighted setting, each vertex in the
network is associated with a nonnegative weight, and the distance from vertex
to is weighted by the weight of . With the strategy of
prune-and-search, we propose a linear time algorithm, which is asymptotically
optimal, to solve the weighted backup 2-center problem on a tree.Comment: 14 pages, 4 figure
An improved quadratic program for unweighted Euclidean 1-center location problem
AbstractIn this paper, an improved quadratic programing formulation for the solution of unweighted Euclidean 1-center location problem is presented. The original quadratic program is proposed by Nair and Chandrasekaran in 1971. Besides, they proposed a geometric approach for problem solving. Then, they concluded that the geometric approach is more efficient than the quadratic program. This conclusion is true only when all decision variables are treated as nonnegative variables. To improve the quadratic program, one of those variables should be an unrestricted variable as it is presented here. Numerically we proved that the improved quadratic program leads to the optimal solution of the problem in parts of second regardless of the size of the problem. Moreover, constrained version of the problem is solved optimally via the improved quadratic program in parts of second
Deaf, Dumb, and Chatting Robots, Enabling Distributed Computation and Fault-Tolerance Among Stigmergic Robot
We investigate ways for the exchange of information (explicit communication)
among deaf and dumb mobile robots scattered in the plane. We introduce the use
of movement-signals (analogously to flight signals and bees waggle) as a mean
to transfer messages, enabling the use of distributed algorithms among the
robots. We propose one-to-one deterministic movement protocols that implement
explicit communication. We first present protocols for synchronous robots. We
begin with a very simple coding protocol for two robots. Based on on this
protocol, we provide one-to-one communication for any system of n \geq 2 robots
equipped with observable IDs that agree on a common direction (sense of
direction). We then propose two solutions enabling one-to-one communication
among anonymous robots. Since the robots are devoid of observable IDs, both
protocols build recognition mechanisms using the (weak) capabilities offered to
the robots. The first protocol assumes that the robots agree on a common
direction and a common handedness (chirality), while the second protocol
assumes chirality only. Next, we show how the movements of robots can provide
implicit acknowledgments in asynchronous systems. We use this result to design
asynchronous one-to-one communication with two robots only. Finally, we combine
this solution with the schemes developed in synchronous settings to fit the
general case of asynchronous one-to-one communication among any number of
robots. Our protocols enable the use of distributing algorithms based on
message exchanges among swarms of Stigmergic robots. Furthermore, they provides
robots equipped with means of communication to overcome faults of their
communication device
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