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Takayuki YATO, Takahiro SETA, "Complexity and Completeness of Finding Another Solution and Its Application to Puzzles" in IEICE TRANSACTIONS on Fundamentals,
vol. E86-A, no. 5, pp. 1052-1060, May 2003, doi: .
Abstract: The Another Solution Problem (ASP) of a problem is the following problem: for a given instance x of and a solution s to it, find a solution to x other than s. The notion of ASP as a new class of problems was first introduced by Ueda and Nagao. They also pointed out that parsimonious reductions which allow polynomial-time transformation of solutions can derive the NP-completeness of ASP of a certain problem from that of ASP of another. In this paper we consider n-ASP, the problem to find another solution when n solutions are given, and formalize it to investigate its characteristics. In particular we consider ASP-completeness, the completeness with respect to the reductions satisfying the properties mentioned above. The complexity of ASPs has a relation with the difficulty of designing puzzles. We prove the ASP-completeness of three popular puzzles: Slither Link, Cross Sum, and Number Place. Since ASP-completeness implies NP-completeness, these results can be regarded as new results of NP-completeness proof of puzzles.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e86-a_5_1052/_p
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@ARTICLE{e86-a_5_1052,
author={Takayuki YATO, Takahiro SETA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Complexity and Completeness of Finding Another Solution and Its Application to Puzzles},
year={2003},
volume={E86-A},
number={5},
pages={1052-1060},
abstract={The Another Solution Problem (ASP) of a problem is the following problem: for a given instance x of and a solution s to it, find a solution to x other than s. The notion of ASP as a new class of problems was first introduced by Ueda and Nagao. They also pointed out that parsimonious reductions which allow polynomial-time transformation of solutions can derive the NP-completeness of ASP of a certain problem from that of ASP of another. In this paper we consider n-ASP, the problem to find another solution when n solutions are given, and formalize it to investigate its characteristics. In particular we consider ASP-completeness, the completeness with respect to the reductions satisfying the properties mentioned above. The complexity of ASPs has a relation with the difficulty of designing puzzles. We prove the ASP-completeness of three popular puzzles: Slither Link, Cross Sum, and Number Place. Since ASP-completeness implies NP-completeness, these results can be regarded as new results of NP-completeness proof of puzzles.},
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - Complexity and Completeness of Finding Another Solution and Its Application to Puzzles
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1052
EP - 1060
AU - Takayuki YATO
AU - Takahiro SETA
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E86-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2003
AB - The Another Solution Problem (ASP) of a problem is the following problem: for a given instance x of and a solution s to it, find a solution to x other than s. The notion of ASP as a new class of problems was first introduced by Ueda and Nagao. They also pointed out that parsimonious reductions which allow polynomial-time transformation of solutions can derive the NP-completeness of ASP of a certain problem from that of ASP of another. In this paper we consider n-ASP, the problem to find another solution when n solutions are given, and formalize it to investigate its characteristics. In particular we consider ASP-completeness, the completeness with respect to the reductions satisfying the properties mentioned above. The complexity of ASPs has a relation with the difficulty of designing puzzles. We prove the ASP-completeness of three popular puzzles: Slither Link, Cross Sum, and Number Place. Since ASP-completeness implies NP-completeness, these results can be regarded as new results of NP-completeness proof of puzzles.
ER -
English
