A 2.75-approximation algorithm for the unconstrained traveling tournament problem

Imahori, Shinji; Matsui, Tomomi; Miyashiro, Ryuhei

doi:10.1007/s10479-012-1161-y

Cited by 18 publications

(20 citation statements)

References 11 publications

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“…Just as various researchers (Imahori et al [9], Thielen and Westphal [15], Westphal and Noparlik [19]) have analyzed these variants for the intra-league TTP, it would be interesting to derive analogous results for the inter-league BTTP, beyond the k = 3 case considered in this paper.…”

Section: Polynomial-time Constructionmentioning

confidence: 98%

“…For k = 2, Thielen and Westphal [15] found a 3 2 + O 1/n approximation. For a fixed k > 3, Westphal and Noparlik [19] determined a 5 875 approximation independent of n and k. And finally, for arbitrary k (i.e., the unconstrained TTP), Imahori et al [9] obtained a 2 75 approximation independent of n.…”

Section: Polynomial-time Constructionmentioning

confidence: 99%

“…In this paper, we answer that question by providing an approximation algorithm for the BTTP, motivated by recent papers that provided approximation algorithms for the general TTP (Miyashiro et al [13], Yamaguchi et al [20]), as well as approximation algorithms for unconstrained TTP variants that considered different options for maximum tour length (Imahori et al [9], Thielen and Westphal [15], Westphal and Noparlik [19]). To do this, we connect the BTTP to the problem of finding a shortest Hamiltonian 721 cycle (i.e., the TSP), as both problems ask for a distance-optimal schedule/route linking venues that are close to one another.…”

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confidence: 99%

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An Approximation Algorithm for the Bipartite Traveling Tournament Problem

Hoshino

Kawarabayashi

2013

Mathematics of OR

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The bipartite traveling tournament problem (BTTP) is an NP-complete scheduling problem whose solution is a double roundrobin inter-league tournament with minimum total travel distance. The 2n-team BTTP is a variant of the well-known traveling salesman problem (TSP), albeit much harder as it involves the simultaneous coordination of 2n teams playing a sequence of home and away games under fixed constraints, rather than a single entity passing through the locations corresponding to the teams' home venues. As the BTTP requires a distance-optimal schedule linking venues in close proximity, we provide an approximation algorithm for the BTTP based on an approximate solution to the corresponding TSP.We prove that our polynomial-time algorithm generates a 2n-team inter-league tournament schedule whose total distance is at most 1 + 2c/3 + 3 − c / 3n times the total distance of the optimal BTTP solution, where c is the approximation factor of the TSP. In practice, the actual approximation factor is far better; we provide a specific example by generating a nearly-optimal inter-league tournament for the 30-team National Basketball Association, with total travel distance just 1 06 times the trivial theoretical lower bound.

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Section: Polynomial-time Constructionmentioning

confidence: 98%

Section: Polynomial-time Constructionmentioning

confidence: 99%

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confidence: 99%

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An Approximation Algorithm for the Bipartite Traveling Tournament Problem

Hoshino

Kawarabayashi

2013

Mathematics of OR

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“…Concerning the constrained SRRT scheduling problem, constraint programming (CP) approach [18] and integer programming (IP) approach [36] were examined in the first half of the 2000s. The problem itself is rather fundamental, and many variants and extensions have been studied so far; e.g., carry-over effect (COE) minimization [14,35], home-away table (HAT) feasibility [5,19,31], double round robin tournament problems such as traveling tournament problem (TTP) [8][9][10]22]. There are some nice reviews for this research field [24,33,34].…”

Section: Problem Plse Inputmentioning

confidence: 99%

An Efficient Local Search for the Constrained Symmetric Latin Square Construction Problem

Haraguchi

2017

JORSJ

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A Latin square is a complete assignment of [n] = {1, . . . , n} to an n × n grid such that, in each row and in each column, each value in [n] appears exactly once. A symmetric Latin square (SLS ) is a Latin square that is symmetric in the matrix sense. In what we call the constrained SLS construction (CSLSC ) problem, we are given a subset F of [n] 3 and are asked to construct an SLS so that, whenever (i, j, k) ∈ F , the symbol k is not assigned to the cell (i, j). This paper has two contributions for this problem. One is proposal of an efficient local search algorithm for the maximization version of the problem. The maximization problem asks to fill as many cells with symbols as possible under the constraint on F . In our local search, the neighborhood is defined by p-swap, i.e., dropping exactly p symbols and then assigning any number of symbols to empty cells. For p ∈ {1, 2}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n p+1 ) time. The other contribution is to show its practical value for the CSLSC problem. For randomly generated instances, our iterated local search algorithm frequently constructs a larger partial SLS than state-of-the-art solvers such as IBM ILOG CPLEX, LocalSolver and WCSP.

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“…The Traveling Tournament Problem (TTP), an interesting sports scheduling problem inspired by Major League Baseball, was first systematically introduced in [Easton et al, 2001], and then followed in a large amount of references [Kendall et al, 2010;Rasmussen and Trick, 2008;Thielen and Westphal, 2012;Xiao and Kou, 2016]. This problem is to find a double round-robin tournament satisfying some constraints that minimizes the total distances traveled by all participant teams.…”

Section: Introductionmentioning

confidence: 99%

The Traveling Tournament Problem with Maximum Tour Length Two: A Practical Algorithm with An Improved Approximation Bound

Zhao

Xiao

2021

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

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The Traveling Tournament Problem is a well-known benchmark problem in tournament timetabling, which asks us to design a schedule of home/away games of n teams (n is even) under some feasibility requirements such that the total traveling distance of all the n teams is minimized. In this paper, we study TTP-2, the traveling tournament problem where at most two consecutive home games or away games are allowed, and give an effective algorithm for n/2 being odd. Experiments on the well-known benchmark sets show that we can beat previously known solutions for all instances with n/2 being odd by an average improvement of 2.66%. Furthermore, we improve the theoretical approximation ratio from 3/2+O(1/n) to 1+O(1/n) for n/2 being odd, answering a challenging open problem in this area.

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A 2.75-approximation algorithm for the unconstrained traveling tournament problem

Cited by 18 publications

References 11 publications

An Approximation Algorithm for the Bipartite Traveling Tournament Problem

An Approximation Algorithm for the Bipartite Traveling Tournament Problem

An Efficient Local Search for the Constrained Symmetric Latin Square Construction Problem

The Traveling Tournament Problem with Maximum Tour Length Two: A Practical Algorithm with An Improved Approximation Bound

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