Edge-Matching Problems with Rotations
Publication: Research - peer-review › Article in proceedings – Annual report year: 2011
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Edge-Matching Problems with Rotations. / Ebbesen, Martin; Fischer, Paul; Witt, Carsten.
In: Fundamentals of Computation Theory: 18th International Symposium, FCT 2011 Oslo, Norway, August 22-25, 2011 Proceedings. Springer, 2011. p. 114-125 (Lecture Notes in Computer Science; No. 6914).Publication: Research - peer-review › Article in proceedings – Annual report year: 2011
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TY - GEN
T1 - Edge-Matching Problems with Rotations
A1 - Ebbesen,Martin
A1 - Fischer,Paul
A1 - Witt,Carsten
AU - Ebbesen,Martin
AU - Fischer,Paul
AU - Witt,Carsten
PB - Springer
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.
UR - http://fct11.ifi.uio.no/
U2 - 10.1007/978-3-642-22953-4
DO - 10.1007/978-3-642-22953-4
SN - 978-3-642-22952-7
BT - Fundamentals of Computation Theory
T2 - Fundamentals of Computation Theory
T3 - Lecture Notes in Computer Science
T3 - en_GB
SP - 114
EP - 125
ER -