## Edge-Matching Problems with Rotations

Publication: Research - peer-review › Article in proceedings – Annual report year: 2011

### Standard

**Edge-Matching Problems with Rotations.** / Ebbesen, Martin; Fischer, Paul; Witt, Carsten.

Publication: Research - peer-review › Article in proceedings – Annual report year: 2011

### Harvard

*Fundamentals of Computation Theory: 18th International Symposium, FCT 2011 Oslo, Norway, August 22-25, 2011 Proceedings.*Springer, pp. 114-125. Lecture Notes in Computer Science, no. 6914, DOI: 10.1007/978-3-642-22953-4

### APA

*Fundamentals of Computation Theory: 18th International Symposium, FCT 2011 Oslo, Norway, August 22-25, 2011 Proceedings.*(pp. 114-125). Springer. (Lecture Notes in Computer Science; No. 6914). DOI: 10.1007/978-3-642-22953-4

### CBE

### MLA

*Fundamentals of Computation Theory: 18th International Symposium, FCT 2011 Oslo, Norway, August 22-25, 2011 Proceedings.*Springer. 2011. 114-125. (Lecture Notes in Computer Science; Journal number 6914). Available: 10.1007/978-3-642-22953-4

### Vancouver

### Author

### Bibtex

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### RIS

TY - GEN

T1 - Edge-Matching Problems with Rotations

AU - Ebbesen,Martin

AU - Fischer,Paul

AU - Witt,Carsten

PY - 2011

Y1 - 2011

N2 - Edge-matching problems, also called puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem has gained interest recently with the (now terminated) Eternity II puzzle, and new complexity results. In this paper we consider a number of settings which differ in size of the puzzles and the manipulations allowed on the pieces. We investigate the effect of allowing rotations of the pieces on the complexity of the problem, an aspect that is only marginally treated so far. We show that some problems have polynomial time algorithms while others are NP-complete. Especially we show that allowing rotations in one-row puzzles makes the problem NP-hard. We moreover show that many commonly considered puzzles can be emulated by simple puzzles with quadratic pieces, so that one can restrict oneself to investigating those.

AB - Edge-matching problems, also called puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem has gained interest recently with the (now terminated) Eternity II puzzle, and new complexity results. In this paper we consider a number of settings which differ in size of the puzzles and the manipulations allowed on the pieces. We investigate the effect of allowing rotations of the pieces on the complexity of the problem, an aspect that is only marginally treated so far. We show that some problems have polynomial time algorithms while others are NP-complete. Especially we show that allowing rotations in one-row puzzles makes the problem NP-hard. We moreover show that many commonly considered puzzles can be emulated by simple puzzles with quadratic pieces, so that one can restrict oneself to investigating those.

U2 - 10.1007/978-3-642-22953-4

DO - 10.1007/978-3-642-22953-4

M3 - Article in proceedings

SN - 978-3-642-22952-7

SP - 114

EP - 125

BT - Fundamentals of Computation Theory

PB - Springer

ER -