Finding a Shortest Solution for the N × N Extension of the 15-PUZZLE Is Intractable
نویسندگان
چکیده
The g-puzzle and the 15puzzle have been used for many years as a domain for testing heuristic search techniques. From experience it is known that these puzzles are “difficult” and therefore useful for testing search techniques. In this paper we give strong evidence that these puzzles are indeed good test problems. We extend the 8puzzle and the Epuzzle to a nxn board and show that finding a shortest solution for the extended puzzle is NP-hard and thus computationally infeasible. We also present an approximation algorithm for transforming boards that is guaranteed to use no more than c%(V) moves, where L(SP) is the length of the shortest solution and c is a constant which is independent of the given boards and their size n .
منابع مشابه
Finding the Shortest Hamiltonian Path for Iranian Cities Using Hybrid Simulated Annealing and Ant Colony Optimization Algorithms
The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...
متن کاملEvaluation of Combined Electro Cutter with Cold Knife in the Intractable Anterior Urethral Stricture Urethrotomy
Background: Sachse cold knife is conventionally used for optical internal urethrotomy to manage urethral strictures. In this procedure, the complications and recurrence rates are relatively high. We suggest combined electro cutter and cold knife as a success alternative in the management of intractable anterior urethral strictures. Methods: In this prospective...
متن کاملThe effect of metformin in the treatment of intractable and late onset acne: a comparison with oral isotretinoin
Background: Insulin resistance and increased insulin-like growth factor (IGF)-1 with consequent mammalian target of rapamycin complex (mTORC) 1 overexpression is responsible for acne pathogenesis, especially in women with polycystic ovary syndrome (PCOS). Metformin is shown to improve acne as an adjunct therapy in females with PCOS and males with altered metabolic profile. We evaluated the use ...
متن کاملSingle-Agent Parallel Window Search: A Summary of Results
We show how node ordering can be combined with parallel window search to quickly find a nearly optimal solution to single-agent problems. First, we show how node ordering by maximum g among nodes with equal / = g + h values can improve the performance of IDA*. We then consider a window search where different processes perform IDA* simultaneously on the same problem but with different cost thres...
متن کاملTwo optimal algorithms for finding bi-directional shortest path design problem in a block layout
In this paper, Shortest Path Design Problem (SPDP) in which the path is incident to all cells is considered. The bi-directional path is one of the known types of configuration of networks for Automated Guided Vehi-cles (AGV).To solve this problem, two algorithms are developed. For each algorithm an Integer Linear Pro-gramming (ILP) is determined. The objective functions of both algorithms are t...
متن کامل