We address the problem of multi-robot area coverage and present a new approach in the case where the map of the area and its static obstacles are known and the robots have a limited visibility range. The proposed method starts by locating a set of static guards on the map of the target area and then builds a graph called Reduced-CDT, a new environment representation method based on the Constrai...

We address the problem of multi-robot area coverage and present a new approach in the case where the map of the area and its static obstacles are known and the robots have a limited visibility range. The proposed method starts by locating a set of static guards on the map of the target area and then builds a graph called Reduced-CDT, a new environment representation method based on the Constrai...

Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P , such that each tour starts and ends in O and covers at most k points from P . The k-tour cover problem is known to be NP-hard. It is al...

The probabilistic traveling salesman problem (PTSP) was introduced by Jaillet [6] as an extension of the classical traveling salesman problem (TSP). In the PTSP, the salesman does not necessarily have to visit every node, but a probability of requiring a visit is given for each node. The goal is to find an a-priori tour that includes every node and minimizes the expected length of an a-posterio...

This article concerns the location of satellite distribution centers (SDCs) to supply humanitarian aid to the affected people throughout a disaster area. In such situations, it is not possible for the relief teams to visit every single home. Instead, the people are required to go to a satellite distribution center in order to obtain survival goods, provided that these centers are not too far fr...

We give a polynomial time algorithm to find the population variance of tour costs over the solution space of the symmetric Traveling Salesman Problem (TSP). In practical terms the algorithm provides a linear time method, on the number of edges of the problem, for determining the standard deviation of these costs. Application of the algorithm has produced empirical evidence that there is a clear...

In the Colorful Traveling Salesman Problem (CTSP), given a graph G with a (not necessarily distinct) label (color) assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the well-known Hamiltonian Cycle problem and has potential applications in telecommunication networks, optical networks, and multimodal transportation networ...

The traveling salesman problem (TSP) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. The TSP is probably the most famous and extensively studied problem in the field of combinatorial optimization. Because this problem is an NP-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...