An Efficient Local Search for Partial Latin Square Extension Problem

A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p in {1,2,3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^{p+1}) time. We also propose a novel swap operation, Trellis-swap, which is a generalization of (1,q)-swap and (2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.Comment: 17 pages, 2 figure

J-POP: Japanese Puzzles as Optimization Problems

Japanese puzzle games such as Sudoku and Futoshiki are familiar recreational pursuits, but they also present an interesting computational challenge. A number of algorithms exist for the automated solution of such puzzles, but, until now, these have not been compared in a unified way. Here we present an integrated framework for the study of combinatorial black-box optimisation, using Japanese puzzles as the test-bed. Importantly, our platform is extendable, allowing for the easy addition of both puzzles and solvers. We compare the performance of a number of optimization algorithms on six different puzzle games, and identify a subset of puzzle instances that could provide a challenging benchmark set for future algorithms

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Global Constraint Catalog, 2nd Edition

This report presents a catalogue of global constraints where each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing filtering algorithms

Global Constraint Catalog, 2nd Edition (revision a)

This report presents a catalogue of global constraints where each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing filtering algorithms

Integer and Constraint programming methods for mutually Orthogonal Latin Squares.

This thesis examines the Orthogonal Latin Squares (OLS) problem from the viewpoint of Integer and Constraint programming. An Integer Programming (IP) model is proposed and the associated polytope is analysed. We identify several families of strong valid inequalities, namely inequalities arising from cliques, odd holes, antiwebs and wheels of the associated intersection graph. The dimension of the OLS polytope is established and it is proved that certain valid inequalities are facet-inducing. This analysis reveals also a new family of facet-defining inequalities for the polytope associated with the Latin square problem. Separation algorithms of the lowest complexity are presented for particular families of valid inequalities. We illustrate a method for reducing problem's symmetry, which extends previously known results. This allows us to devise an alternative proof for the non-existence of an OLS structure for n = 6, based solely on Linear Programming. Moreover, we present a more general Branch & Cut algorithm for the OLS problem. The algorithm exploits problem structure via integer preprocessing and a specialised branching mechanism. It also incorporates families of strong valid inequalities. Computational analysis is conducted in order to illustrate the significant improvements over simple Branch & Bound. Next, the Constraint Programming (CP) paradigm is examined. Important aspects of designing an efficient CP solver, such as branching strategies and constraint propagation procedures, are evaluated by comprehensive, problem-specific, experiments. The CP algorithms lead to computationally favourable results. In particular, the infeasible case of n = 6, which requires enumerating the entire solution space, is solved in a few seconds. A broader aim of our research is to successfully integrate IP and CP. Hence, we present ideas concerning the unification of IP and CP methods in the form of hybrid algorithms. Two such algorithms are presented and their behaviour is analysed via experimentation. The main finding is that hybrid algorithms are clearly more efficient, as problem size grows, and exhibit a more robust performance than traditional IP and CP algorithms. A hybrid algorithm is also designed for the problem of finding triples of Mutually Orthogonal Latin Squares (MOLS). Given that the OLS problem is a special form of an assignment problem, the last part of the thesis considers multidimensional assignment problems. It introduces a model encompassing all assignment structures, including the case of MOLS. A necessary condition for the existence of an assignment structure is revealed. Relations among assignment problems are also examined, leading to a proposed hierarchy. Further, the polyhedral analysis presented unifies and generalises previous results

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum