ICALP 1984: Automata, Languages and Programming pp 119-127

# The complexity and decidability of separation

• Bernard Chazelle
• Thomas Ottmann
• Eljas Soisalon-Soininen
• Derick Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 172)

## Abstract

We study the difficulty of solving instances of a new family of sliding block puzzles called SEPARATIONTM. Each puzzle in the family consists of an arrangement in the plane of n rectilinear wooden blocks, n > 0. The aim is to discover a sequence of rectilinear moves which when carried out will separate each piece to infinity. If there is such a sequence of moves we say the puzzle or arrangement is separable and if each piece is moved only once we say it is one-separable. Furthermore if it is one-separable with all moves being in the same direction we say it is iso-separable.

We prove:
1. (1)

There is an O(n log n) time algorithm to decide whether or not a puzzle is iso-separable, where the blocks have a total of n edges.

2. (2)

There is an O(n log2n) time algorithm to decide whether or not a puzzle is one-separable.

3. (3)

It is decidable whether or not a puzzle is separable.

4. (4)

Deciding separability is NP-hard.

5. (5)

There are puzzles which require time exponential in the number of edges to separate them.

## Keywords

Move Sequence Segment Tree Computer Science Technical Report Proper Ancestor Relation Trap
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Bernard Chazelle
• 1
• Thomas Ottmann
• 2
• Eljas Soisalon-Soininen
• 3
• Derick Wood
• 4
1. 1.Computer Science DepartmentBrown UniversityProvidenceUSA
2. 2.Institut für Angewandte Informatik und Formale BeschreibungsverfahrenUniversität KarlsruheKarlsruheW. Germany
3. 3.Department of Computer ScienceUniversity of HelsinkiHelsinki 25Finland
4. 4.Data Structuring Group, Department of Computer ScienceUniversity of WaterlooWaterlooCanada