## SOKOBAN and other motion planning problems (Extended Abstract) (1995)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Dor95sokobanand,

author = {Dorit Dor and Uri Zwick},

title = {SOKOBAN and other motion planning problems (Extended Abstract)},

year = {1995}

}

### OpenURL

### Abstract

We consider a natural family of motion planning problems with movable obstacles and obtain hardness results for them. Some members of the family are shown to be PSPACE-complete thus improving and extending (and also simplifying) a previous NP-hardness result of Wilfong. The family considered includes a motion planning problem which forms the basis of a popular computer game called SOKOBAN. The decision problem corresponding to SOKOBAN is shown to be NP-hard. The motion planning problems considered are related to the "warehouseman's problem" considered by Hopcroft, Schwartz and Sharir, and to geometric versions of the motion planning problem on graphs considered by Papadimitriou, Raghavan, Sudan and Tamaki.

### Citations

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(Show Context)
Citation Context ... solution. We show that this problem is NP-hard. It is an interesting open problem whether this problem is in NP. It is clearly contained in nondeterministic PSPACE and therefore, by Savitch's result =-=[Sav70]-=-, also in PSPACE. We let SOKOBAN(k; `) be the following generalisation of SOKOBAN. The packets are still 1 \Theta 1 squares but the porter is now powerful enough to push up to k packets at once. She c... |

250 |
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(Show Context)
Citation Context ...ts and obstacles should never overlap. Various forms of motion planning problems were already considered by many researchers. Geometric motion planning problems were considered, among others, by Reif =-=[Rei79]-=-, Hopcroft, Schwartz and Sharir [HSS84] and Wilfong [Wil88]. A motion planning on graphs which forms an abstraction of such problems was considered by Papadimitriou, Raghavan, Sudan and Tamaki [PRST94... |

192 |
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(Show Context)
Citation Context ...nterpreted modulo n. The graph G I contains an edge between each variable x and each clause that contain either x or x. It also contains a simple cycle passing through all the variables. Lichtenstein =-=[Lic82]-=- showed that the P3SAT problem is NPC. Moreover, he showed [Lic82] that the P3SAT problem is NPC even when, at every variable vertex x, all edges representing positive instances of the variable are in... |

73 |
Motion planning in the presence of movable obstacles
- Wilfong
- 1988
(Show Context)
Citation Context ...ion planning problems were already considered by many researchers. Geometric motion planning problems were considered, among others, by Reif [Rei79], Hopcroft, Schwartz and Sharir [HSS84] and Wilfong =-=[Wil88]-=-. A motion planning on graphs which forms an abstraction of such problems was considered by Papadimitriou, Raghavan, Sudan and Tamaki [PRST94]. In this work we consider a family of motion planning pro... |

6 |
A Subway Named Turing
- Stewart
- 1994
(Show Context)
Citation Context ...riginal position and all gates in their closed position. The general structure of the above construction is similar to the general structure of a construction by Chalcraft and Greene [CG94] (see also =-=[Ste94]-=-). Chalcraft and Greene describe a simulation of a Turing machine using train sets. 3 NP-hardness of SOKOBAN(1; 1) In this section we show that SOKOBAN(5,1) is NP-hard. Recall that in this version of ... |

3 |
Train sets
- Chalcraft, Greene
- 1994
(Show Context)
Citation Context ...sovers in their original position and all gates in their closed position. The general structure of the above construction is similar to the general structure of a construction by Chalcraft and Greene =-=[CG94]-=- (see also [Ste94]). Chalcraft and Greene describe a simulation of a Turing machine using train sets. 3 NP-hardness of SOKOBAN(1; 1) In this section we show that SOKOBAN(5,1) is NP-hard. Recall that i... |

3 |
Motion planning on a graph (extended abstract
- Papadimitriou, Raghavan, et al.
- 1994
(Show Context)
Citation Context ...[Rei79], Hopcroft, Schwartz and Sharir [HSS84] and Wilfong [Wil88]. A motion planning on graphs which forms an abstraction of such problems was considered by Papadimitriou, Raghavan, Sudan and Tamaki =-=[PRST94]-=-. In this work we consider a family of motion planning problems obtained by generalising the rules of a computer game called SOKOBAN. 1 A typical level of SOKOBAN is shown in Figure 1. Each level is c... |

2 |
On the complexity of motion planning for multiple indepandant objects; PSPACE-hardness of the "Warehouseman's problem
- Hopcroft, Schwartz, et al.
- 1984
(Show Context)
Citation Context ...Various forms of motion planning problems were already considered by many researchers. Geometric motion planning problems were considered, among others, by Reif [Rei79], Hopcroft, Schwartz and Sharir =-=[HSS84]-=- and Wilfong [Wil88]. A motion planning on graphs which forms an abstraction of such problems was considered by Papadimitriou, Raghavan, Sudan and Tamaki [PRST94]. In this work we consider a family of... |