SOLVING THE LONGEST WORD-CHAIN PROBLEM

Nobuo Inui, Yuji Shinano, Yuusuke Kounoike, Yoshiyuki Kotani

Abstract

The SHIRITORI game is a traditional Japanese word-chain game. This paper describes the definition of the longest SHIRITORI problem (a kind of the longest distance problem) as a problem of graph and the solution based on the integer problem (IP). This formulation requires the exponential order variables from the problem size. Against this issue, we propose a solution based on the LP-based branch-and-bound method, which solves the relaxation problems repeatedly. This method is able to calculate the longest SHIRITORI sequences for 130 thousand words dictionary within a second. In this paper, we compare the performances for the heuristic-local search and investigate the results for several conditions to explore the longest SHIRITORI problem.

References

  1. Abe, K., Araya, S., 1986. Train Traffic Simulation Using the Longest Path Method. T.of IPSJ, Vol.27, No.1, pp.103-111.
  2. Gu, Q-P., Takaoka, T., 1996. A Parallel Algorith for the Longest Paths Problem on Acyclic Graphs with Integer Arc Length. T.of IPSJ,Vol.37, No.9,pp.1631-1636.
  3. Fischetti, M., Salazar-Gonzalez, J-J., Toth, P., 2002. The Genralized Traveling Salesman Problem and Orienteering Problems in The Generalized Traveling Salesman Problem and its Variations. Kluwer Academic Publisher.
  4. Ito, T., Tanaka, T., Hu, H., Takeuchi, M., 2002. An Analysis of Word Chain Games. J.of IPSJ, Vol.43 No.10
  5. Kanasugi, T., Matsuzawa, K., Kasahara K., 1996. Applications of ABOUT Reasoning to Solving Wordplays. TR.of IEICE, NLC96-31, pp.1-8.
  6. Lai, H-J., 2001. Eulerian Subgraphs Containing given Edges, Discrete Mathematics, 230, pp.63-69.
  7. Li, Dengxin, Li, Deying, Mao, J., 2004. On Maximum number of Edges in a spanning Eulerian Subgraph, Discrete Mathematics, 274, pp.299-302.
  8. Nakayama, S., Masuyama, S., 1995. A Parallel Algorithm for Solving the Longest Path Problem in Outerplannar Graphs, IEICE Transaction D-I, Vol.J'-D-I, No.6, pp.563-568.
  9. Niimura, I. (eds), 1992. Koujien Ver.4, Iwanami
  10. Sosic, R., Gu, J., 1990. A Polynomial Time Algorithm to the N-Queen Problem. SIGART, 1, pp.7-11
  11. Skina, S., 1990. Eulerian Cycles. In Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Addison-Wesley.
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Paper Citation


in Harvard Style

Inui N., Shinano Y., Kounoike Y. and Kotani Y. (2004). SOLVING THE LONGEST WORD-CHAIN PROBLEM . In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 972-8865-12-0, pages 214-221. DOI: 10.5220/0001138902140221


in Bibtex Style

@conference{icinco04,
author={Nobuo Inui and Yuji Shinano and Yuusuke Kounoike and Yoshiyuki Kotani},
title={SOLVING THE LONGEST WORD-CHAIN PROBLEM},
booktitle={Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2004},
pages={214-221},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001138902140221},
isbn={972-8865-12-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - SOLVING THE LONGEST WORD-CHAIN PROBLEM
SN - 972-8865-12-0
AU - Inui N.
AU - Shinano Y.
AU - Kounoike Y.
AU - Kotani Y.
PY - 2004
SP - 214
EP - 221
DO - 10.5220/0001138902140221