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A compositeneighborhood tabu search approach to the travelling tournament problem
 Journal of Heuristics
, 2007
"... The Traveling Tournament Problem (TTP) is a combinatorial problem that combines features from the traveling salesman problem and the tournament scheduling problem. We propose a family of tabu search solvers for the solution of TTP that make use of complex combination of many neighborhood structures. ..."
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The Traveling Tournament Problem (TTP) is a combinatorial problem that combines features from the traveling salesman problem and the tournament scheduling problem. We propose a family of tabu search solvers for the solution of TTP that make use of complex combination of many neighborhood structures. The different neighborhoods have been thoroughly analyzed and experimentally compared. We evaluate the solvers on three sets of publicly available benchmarks and we show a comparison of their outcomes with previous results presented in the literature. The results show that our algorithm is competitive with those in the literature.
Onefactorizations of regular graphs of order 12
 The Electronic Journal of Combinatorics
"... Algorithms for classifying onefactorizations of regular graphs are studied. The smallest open case is currently graphs of order 12; onefactorizations of rregular graphs of order 12 are here classified for r ≤ 6andr = 10, 11. Two different approaches are used for regular graphs of small degree; th ..."
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Algorithms for classifying onefactorizations of regular graphs are studied. The smallest open case is currently graphs of order 12; onefactorizations of rregular graphs of order 12 are here classified for r ≤ 6andr = 10, 11. Two different approaches are used for regular graphs of small degree; these proceed onefactor by onefactor and vertex by vertex, respectively. For degree r = 11, we have onefactorizations of K12. These have earlier been classified, but a new approach is presented which views these as certain triple systems on 4n − 1 points and utilizes an approach developed for classifying Steiner triple systems. Some properties of the classified onefactorizations are also tabulated. 1
On the Application of Graph Colouring Techniques in RoundRobin Sports Scheduling
, 2010
"... The purpose of this paper is twofold. First, it explores the issue of producing valid, compact roundrobin sports schedules by considering the problem as one of graph colouring. Using this model, which can also be extended to incorporate additional constraints, the difficulty of such problems is the ..."
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The purpose of this paper is twofold. First, it explores the issue of producing valid, compact roundrobin sports schedules by considering the problem as one of graph colouring. Using this model, which can also be extended to incorporate additional constraints, the difficulty of such problems is then gauged by considering the performance of a number of different graph colouring algorithms. Second, neighbourhood operators are then proposed that can be derived from the underlying graph colouring model and, in an example application, we show how these operators can be used in conjunction with multiobjective optimisation techniques to produce highquality solutions to a realworld sports league scheduling problem encountered at the Welsh Rugby Union in Cardiff, Wales. 1
CONTINUOUS RANDOM CUBE PACKINGS IN CUBE AND TORUS
, 805
"... Abstract. We consider sequential random packing of integral translate of cubes [0, N] n into the cube [0, 2N] n and the torus Zn /2NZ n as N → ∞. In the rigid boundary case [0, 2N] n continuous cube packing are reduced to a single cube with probability 1 − O ( 1 N+1); more generally we obtain the ex ..."
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Abstract. We consider sequential random packing of integral translate of cubes [0, N] n into the cube [0, 2N] n and the torus Zn /2NZ n as N → ∞. In the rigid boundary case [0, 2N] n continuous cube packing are reduced to a single cube with probability 1 − O ( 1 N+1); more generally we obtain the expansion of the packing
Article electronically published on September 13, 2010 THE NUMBER OF LATIN SQUARES OF ORDER 11
"... Abstract. Constructive and nonconstructive techniques are employed to enumerate Latin squares and related objects. It is established that there are (i) 2036029552582883134196099 main classes of Latin squares of order 11; (ii) 6108088657705958932053657 isomorphism classes of onefactorizations of K11 ..."
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Abstract. Constructive and nonconstructive techniques are employed to enumerate Latin squares and related objects. It is established that there are (i) 2036029552582883134196099 main classes of Latin squares of order 11; (ii) 6108088657705958932053657 isomorphism classes of onefactorizations of K11,11; (iii) 12216177315369229261482540 isotopy classes of Latin squares of order 11; (iv) 1478157455158044452849321016 isomorphism classes of loops of order 11; and (v) 19464657391668924966791023043937578299025 isomorphism classes of quasigroups of order 11. The enumeration is constructive for the 1151666641 main classes with an autoparatopy group of order at least 3. 1.
A census of onefactorizations of the complete 3uniform hypergraph of order 9
"... The onefactorizations of the complete 3uniform hypergraph with 9 vertices, K 3 9, are classified by means of an exhaustive computer search. It is shown that the number of isomorphism classes of such onefactorizations is 103 000. 1 ..."
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The onefactorizations of the complete 3uniform hypergraph with 9 vertices, K 3 9, are classified by means of an exhaustive computer search. It is shown that the number of isomorphism classes of such onefactorizations is 103 000. 1