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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

Sivakumar Rathinam, Sengupta, Sivakumar Rathinam, Raja Sengupta, Sivakumar Rathinam, Raja Sengupta
2007 unpublished
We consider 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 2approximation ratio.  ... 

A PTAS for the Min-Max Euclidean Multiple TSP [article]

Mary Monroe
2021 arXiv   pre-print
We present 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.  ... 
arXiv:2112.04325v2 fatcat:u67tvjt6lvhdzoeu6mdfr4aoyi

Approximation algorithms for a heterogeneous Multiple Depot Hamiltonian Path Problem

S. Yadlapalli, Jungyun Bae, S. Rathinam, S. Darbha
2011 Proceedings of the 2011 American Control Conference  
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  ...  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 2approximation 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.  ... 
doi:10.1109/acc.2011.5991534 fatcat:vseqmw5rybasnfreoyrkjqg4mi

Efficient Approximations for Many-Visits Multiple Traveling Salesman Problems [article]

Kristóf Bérczi and Matthias Mnich and Roland Vincze
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.  ... 
arXiv:2201.02054v1 fatcat:iczagzqkwjfm5eqq22siyrlbgm

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]

Markus Bläser, Konstatinos Panagiotou, B. V. Raghavendra Rao
2012 Lecture Notes in Computer Science  
Christofides' 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.  ... 
doi:10.1007/978-3-642-31155-0_20 fatcat:2ewyq64tbnca5dex34eukntwmy

A polynomial-time algorithm for the routing flow shop problem with two machines: an asymmetric network with a fixed number of nodes [article]

Ilya Chernykh, Alexander Kononov, Sergey Sevastyanov
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.  ... 
arXiv:2004.03942v2 fatcat:tcedhsypzzf57kf7dkufelghja

Consolidation and coordination of routes in urban distribution

Andrea Mor
2019 4OR  
Viegas 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.  ... 
doi:10.1007/s10288-019-00400-6 fatcat:dq5uwagfuje5dhqyqlksm4hb54

Multirobot Coverage of Linear Modular Environments [article]

Mirko Salaris Politecnico di Milano)
2020 arXiv   pre-print
The 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  ... 
arXiv:2001.02906v1 fatcat:h5o7udzr4rfetowjs4hsxvdr6q

Polynomial-Time Approximation Schemes for k-center, k-median, and Capacitated Vehicle Routing in Bounded Highway Dimension

Amariah Becker, Philip N. Klein, David Saulpic, Michael Wagner
2018 European Symposium on Algorithms  
This result implies 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.  ... 
doi:10.4230/lipics.esa.2018.8 dblp:conf/esa/BeckerKS18 fatcat:tbquhn36jzhajdt7u36ti3mo5m

Optimal Charging Oriented Sensor Placement and Flexible Scheduling in Rechargeable WSNs

Tao Wu, Panlong Yang, Haipeng Dai, Chaocan Xiang, Wanru Xu
2022 ACM transactions on sensor networks  
Thus, 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.  ... 
doi:10.1145/3512888 fatcat:5ww3wcpu7nauhispxwkph7h3mu

Planning for Aerial Robot Teams for Wide-Area Biometric and Phenotypic Data Collection [article]

Tianshuang Gao, Shashwata Mandal, Sourabh Bhattacharya
2020 arXiv   pre-print
This work presents an efficient and implementable solution to the 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] .  ... 
arXiv:2011.01492v1 fatcat:o2nmd4zlbvephf7userxuigype

Approximation Algorithms for Multi-Robot Patrol-Scheduling with Min-Max Latency [article]

Peyman Afshani, Mark De Berg, Kevin Buchin, Jie Gao, Maarten Loffler, Amir Nayyeri, Benjamin Raichel, Rik Sarkar, Haotian Wang, Hao-Tsung Yang
2020 arXiv   pre-print
The 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  ... 
arXiv:2005.02530v3 fatcat:wgu22smplbbdxcezky45wgndnq

A Tight (3/2+ϵ)-Approximation for Unsplittable Capacitated Vehicle Routing on Trees [article]

Claire Mathieu, Hang Zhou
2022 arXiv   pre-print
We give 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.  ... 
arXiv:2202.05691v1 fatcat:vnaikpwswzh3pdotmr4jha4gda

Approximations for minimum and min-max vehicle routing problems

Esther M. Arkin, Refael Hassin, Asaf Levin
2006 Journal of Algorithms  
The goal here is to minimize λ, the maximum 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.  ... 
doi:10.1016/j.jalgor.2005.01.007 fatcat:dfzdsajzwvhttcthk5apktmck4
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