Approximation algorithms for a heterogeneous Multiple Depot Hamiltonian Path Problem

Abstract

In this article, we present the first approximation algorithm for a routing problem that is frequently encountered in the motion planning of Unmanned Vehicles (UVs). The considered problem is a variant of a Multiple Depot-Terminal Hamiltonian Path Problem and is stated as follows: There is a collection of m UVs equipped with different sensors on-board and there are n targets to be visited by them collectively. There are restrictions on the targets of the following type: (1) A target may be visited by any UV, (2) a target must be visited only by a subset of UVs (with appropriate on-board sensor) and (3) a target may not be visited by a subset of UVs (as the set of onboard sensors on the UV may not be suitable for viewing the targets). The UVs are otherwise identical from the viewpoint of dynamic constraints on their motion and hence, the cost of traveling from a target A to a target B is the same for all vehicles. We will assume that triangle inequality is satisfied by the cost associated with travel, i.e., it is cheaper to travel from a target A to a target B directly than to go via an intermediate target C. The UVs may possibly start from different locations (referred to as depots) and are not required to return to the depot. While there are different objectives that can be considered for this problem, we consider the total cost of travel of all the UVs as an objective to be minimized. The problem considered in this article is a generalized version of single depot-terminal Hamiltonian Path Problem and is NP-hard.

Distributed Approximation Algorithms for the Combinatorial Motion Planning Problem

“…In this article we will present a 4 factor approximation algorithm for the Combinatorial Motion Planning problem and then subsequently present the first fully distributed algorithm for CMP in asynchronous message passing systems. Though our algorithm gives a worse approximation factor in centralized systems, we show that we would obtain better a approximation factor compared to a distributed version of the algorithm presented by Yadlapalli et al [18]. Specifically, we show that a distributed version of the algorithm by Yadlapalli et al [18] would give an approximation factor of 13 3 due to lack of exact distributed algorithms for minimum cost matching.…”

“…al. [18] present a 11 3 factor approximation algorithm for the Combinatorial Motion Planning problem (CMP). In this article we will present a 4 factor approximation algorithm for the Combinatorial Motion Planning problem and then subsequently present the first fully distributed algorithm for CMP in asynchronous message passing systems.…”

“…al. [18] but differs in respect to the fact that it does not require us to use minimum cost matching as a subroutine, and hence can be easily distributed.…”

Efficient path planning for multiple transportation robots under various loading conditions

“…Only few articles considered functional heterogeneity for vehicle routing problems. Sundar and Rathinam 3 and Yadlapalli et al 4 addressed functional heterogeneity for multiple HPPs. Both articles attempted to resolve the issue of functional heterogeneity by assigning specified targets to each vehicle and forbidding other vehicles from visiting these preassigned targets.…”

A Primal-Dual Heuristic for a Heterogeneous Unmanned Vehicle Path Planning Problem

“…For example, Doshi et al [8] present heuristics and an approximation algorithm for a 2-depot, symmetric HPP. Approximation algorithms are presented for a multiple depot, symmetric HPP in [20]. A heuristic based on a transformation method is also presented for a multiple depot, asymmetric, heterogeneous TSP by Oberlin et al in [15].…”