Toni Mancini

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Evaluating ASP and commercial solvers on the CSPLib

Toni Mancini, Davide Micaletto, Fabio Patrizi, Marco Cadoli
Dipartimento di Informatica e Sistemistica
Università di Roma "La Sapienza"
via Salaria 113, I-00198 Roma, Italy

Appeared in Constraints, 13(4), pages 407-436, 2008.

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Problem description

An order 'n' magic square is a 'n' by 'n' matrix containing the numbers 1 to n², with each row, column and main diagonal equal the same sum. Given a positive integer 'n', the problem amounts to find a 'n' order magic square.

Problem input

n, the order of the magic square to find

Search space

The set of all possible assignments of integers from 1 to n² to the n² entries of the matrix

Constraints

C1: Numbers assigned to entries of the matrix must be all different
C2: Each row, column and main diagonal equal the same sum

Problem specifications

Specification	OPL	DLV	LPARSE
BASE: Base specification	View	View	View
SBSA: Symmetry-breaking by selective assignment	View	View	View
SBLI: Symmetry-breaking by lowest index ordering	View	View	View
SBSO: Symmetry-breaking by selective ordering	View	View	View
AUX: Addition of auxiliary predicates	View	View	View
GCAD: Exploitation of alldifferent() global constraint	View	--	--
AUX-SBSA: Addition of auxiliary predicates plus Symmetry-breaking by selective assignment	View	View	View
AUX-SBLI: Addition of auxiliary predicates plus Symmetry-breaking by lowest index ordering	View	View	View
AUX-GCAD: Addition of auxiliary predicates plus Exploitation of alldifferent() global constraint	View	--	--
AUX-GCAD-SBLI: Addition of auxiliary predicates plus Exploitation of alldifferent() global constraint plus Symmetry-breaking by lowest index ordering	View	--	--

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