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UC Berkeley Research Reports Title 3/2-Approximation Algorithm for a Generalized, Multiple Depot, Hamiltonina Path Problem 3/2-Approximation Algorithm for a Generalized, Multiple Depot, Hamiltonian Path Problem 3 2 −Approximation Algorithm for a Generalized, Multiple Depot Hamiltonian Path Problem

2007
unpublished

We consider

fatcat:lvfqzn22e5gepbgrcgp44nknz4
*a*Generalized,*Multiple**Depot*Hamiltonian Path*Problem*(GMDHPP) and show that it has an*algorithm*with an approximation ratio of 3 2 if the costs are symmetric and satisfy the triangle inequality ... This improves on the 2-approximation*algorithm*already available*for*the same. ... This helps us prove that the*algorithm*presented above*for*GMDHPP has*a**3**2*−*approximation*ratio. ...##
###
A PTAS for the Min-Max Euclidean Multiple TSP
[article]

2021
*
arXiv
*
pre-print

We present

arXiv:2112.04325v2
fatcat:u67tvjt6lvhdzoeu6mdfr4aoyi
*a*polynomial-time approximation scheme (PTAS)*for*the min-max*multiple*TSP*problem*in Euclidean space, where*multiple**traveling*salesmen are tasked with visiting*a*set of n points and the objective ... Our*algorithm*introduces*a*rounding process to balance the allocation of path lengths among the*multiple**salesman*. ...*A**3*/*2*-*approximation**algorithm**for**multiple**depot**multiple**traveling**salesman**problem*. In Proc. 12th Scand. ...##
###
Approximation algorithms for a heterogeneous Multiple Depot Hamiltonian Path Problem

2011
*
Proceedings of the 2011 American Control Conference
*

The considered

doi:10.1109/acc.2011.5991534
fatcat:vseqmw5rybasnfreoyrkjqg4mi
*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 ... 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). ...*A**3**2*−*approximation**algorithm*was also developed*for*two variants of*a*2-*depot*Hamiltonian path*problem*in [8] when the the costs are symmetric and satisfy the triangle inequality. ...##
###
Efficient Approximations for Many-Visits Multiple Traveling Salesman Problems
[article]

2022
*
arXiv
*
pre-print

*A*fundamental variant of the classical

*traveling*

*salesman*

*problem*(TSP) is the so-called

*multiple*TSP (mTSP), where

*a*set of m salesmen jointly visit all cities from

*a*set of n cities. ... We provide

*multiple*efficient approximation

*algorithms*

*for*important variants of the many-visits mTSP, which are guaranteed to quickly compute high-quality solutions

*for*all

*problem*instances. ... [5] , that were used to obtain

*a*polynomial-time

*3*/

*2*-

*approximation*

*for*the metric Many-Visits Path TSP. ...

##
###
Page 3497 of Mathematical Reviews Vol. , Issue 2001E
[page]

2001
*
Mathematical Reviews
*

As

*a*corollary, the authors note that*a*network consisting of*a*Hamiltonian cycle constructed using Christofides’*3*/*2**approximation**algorithm*along with*a*minimum spanning tree yields*a*polynomial 5//3 ... This obviously involves solving an ATSP (asymmetric*travelling**salesman**problem*) on the subgraph induced by the customers assigned to the same*depot*. ...##
###
A Probabilistic Analysis of Christofides' Algorithm
[chapter]

2012
*
Lecture Notes in Computer Science
*

Christofides'

doi:10.1007/978-3-642-31155-0_20
fatcat:2ewyq64tbnca5dex34eukntwmy
*algorithm*is*a*well known approximation*algorithm**for*the metric*travelling**salesman**problem*. ... As*a*first step towards obtaining an average case analysis of Christofides'*algorithm*, we provide*a*probabilistic analysis*for*the stochastic version of the*algorithm**for*the Euclidean*traveling**salesman*... We obtain*a*TSP tour by taking shortcuts in the Eulerian tour.*For*arbitrary metrics, Christofides'*algorithm*achieves*a**3*/*2*-*approximation*. ...##
###
A polynomial-time algorithm for the routing flow shop problem with two machines: an asymmetric network with a fixed number of nodes
[article]

2020
*
arXiv
*
pre-print

*For*this

*problem*we discuss properties of an optimal schedule and present

*a*polynomial time

*algorithm*assuming the number of nodes of the network to be bounded by

*a*constant. ... To the best of our knowledge, this is the first positive result on the complexity of the routing flow shop

*problem*with an arbitrary structure of the transportation network, even in the case of

*a*symmetric ... Now,

*for*proving 2

*3*

*2*)-

*approximation*

*algorithm*based on

*a*reduction of the original

*problem*to the permutation flow shop

*problem*. ...

##
###
Consolidation and coordination of routes in urban distribution

2019
*
4OR
*

Viegas

doi:10.1007/s10288-019-00400-6
fatcat:dq5uwagfuje5dhqyqlksm4hb54
*for*sharing his experience on real world*problems*. ... Finally, I wish to thank all the members of the OR group at the University of Brescia*for*welcoming me so warmly and*for*making even the most relaxed moment an occasion*for*learning and sharing. ... Solution Approximation*algorithm*The following approximation*algorithm**for*the TSP-rd(time) relies on the well-known Christofides*3**2*-*approximation**algorithm**for*the TSP. ...##
###
Multirobot Coverage of Linear Modular Environments
[article]

2020
*
arXiv
*
pre-print

The

arXiv:2001.02906v1
fatcat:h5o7udzr4rfetowjs4hsxvdr6q
*problem*of covering*a*given environment using*multiple*robots can be naturally formulated and studied as*a*multi-*Traveling*Salesperson*Problem*(mTSP). ... The mTSP is an NP-hard*problem**for*which several approximation*algorithms*have been proposed. ...*For*example, [16] provides an*algorithm*with*a*constant approximation factor of 2*for*the Generalized,*Multiple**Depot*,*Multiple**Traveling**Salesman**Problem*(GMTSP), where the objective is to minimize ...##
###
Polynomial-Time Approximation Schemes for k-center, k-median, and Capacitated Vehicle Routing in Bounded Highway Dimension

2018
*
European Symposium on Algorithms
*

This result implies

doi:10.4230/lipics.esa.2018.8
dblp:conf/esa/BeckerKS18
fatcat:tbquhn36jzhajdt7u36ti3mo5m
*a*PTAS*for**Multiple**Depot*Bounded-Capacity Vehicle Routing: the tours can go from one*depot*to another. ... In this*problem*, the input specifies*a**depot*and*a*set of clients, each with*a*location and demand; the output is*a*set of*depot*-to-*depot*tours, where each client is visited by some tour and each tour ... Acknowledgements Thanks to Andreas Feldmann and Vincent Cohen-Addad*for*helpful discussions and comments. ...##
###
Optimal Charging Oriented Sensor Placement and Flexible Scheduling in Rechargeable WSNs

2022
*
ACM transactions on sensor networks
*

Thus,

doi:10.1145/3512888
fatcat:5ww3wcpu7nauhispxwkph7h3mu
*a*constant approximation*algorithm*is delivered to construct*a*near optimal charging tour. ... In particular, we formulate*a*general maximization optimization*problem*under*a*general routing constraint, which generates great difficulty. ...*For*example, another*3*/*2*-*approximation**algorithm*based on the minimum spanning tree can be devised referring to [5] and () is 3/2. ...##
###
Planning for Aerial Robot Teams for Wide-Area Biometric and Phenotypic Data Collection
[article]

2020
*
arXiv
*
pre-print

This work presents an efficient and implementable solution to the

arXiv:2011.01492v1
fatcat:o2nmd4zlbvephf7userxuigype
*problem*of joint task allocation and path planning in*a*multi-UAV platform deployed*for*biometric data collection in-the-wild. ... As*a*tangible solution to the allocation*problem*, we use*a*clustering-based technique that incorporates temporal uncertainty in the cardinality and position of the robots. ... Even though ∆-T SP is known to be NP-Hard [31] , the Christofides'*algorithm*provides*a**3**2**approximation**algorithm**for*∆-T SP [32] . ...##
###
Approximation Algorithms for Multi-Robot Patrol-Scheduling with Min-Max Latency
[article]

2020
*
arXiv
*
pre-print

The

arXiv:2005.02530v3
fatcat:wgu22smplbbdxcezky45wgndnq
*problem*is NP-hard, as it has the*traveling**salesman**problem*as*a*special case (when k=1 and all sites have the same weight). ... We consider the*problem*of finding patrol schedules*for*k robots to visit*a*given set of n sites in*a*metric space. ... There are efficient approximation*algorithms**for*TSP, namely,*a*(*3*/*2*)-*approximation**for*metric TSP [8] and*a*polynomial-time approximation scheme (PTAS)*for*Euclidean TSP [4, 23] , which carry over ...##
###
A Tight (3/2+ϵ)-Approximation for Unsplittable Capacitated Vehicle Routing on Trees
[article]

2022
*
arXiv
*
pre-print

We give

arXiv:2202.05691v1
fatcat:vnaikpwswzh3pdotmr4jha4gda
*a*polynomial time (3/2+ϵ)-approximation*algorithm**for*the unsplittable capacitated vehicle routing*problem*(CVRP) on trees. ... Our approximation ratio is tight, given that it is NP-hard to approximate this*problem*to better than*a*3/2 factor. ...*For*any > 0, there is*a*polynomial time (*3*/*2*+ )-*approximation**algorithm**for*the unsplittable capacitated vehicle routing*problem*(CVRP) on trees. ...##
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Approximations for minimum and min-max vehicle routing problems

2006
*
Journal of Algorithms
*

The goal here is to minimize λ, the maximum

doi:10.1016/j.jalgor.2005.01.007
fatcat:dfzdsajzwvhttcthk5apktmck4
*travel*distance.*For*all these*problems*we provide constant ratio approximation*algorithms*and prove their NP-hardness. ... We consider*a*variety of vehicle routing*problems*. The input to*a**problem*consists of*a*graph G = (N, E) and edge lengths l(e) e ∈ E. ... Output:*A*walk P such that E ⊂ P . measure: l(P ). The*problem*is NP-hard [14] and has*a**3**2*-*approximation**algorithm*[10] . Previous work. ...
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