Space bounds for a game on graphs

Wolfgang J. Paul; Robert Endre Tarjan; James R. Celoni

doi:10.1007/BF01683275

Space bounds for a game on graphs

Wolfgang J. Paul, Robert Endre Tarjan, James R. Celoni

Research output: Contribution to journal › Article › peer-review

91 Scopus citations

Abstract

We study a one-person game played by placing pebbles, according to certain rules, on the vertices of a directed graph. In [3] it was shown that for each graph with n vertices and maximum in-degree d, there is a pebbling strategy which requires at most c(d) n/log n pebbles. Here we show that this bound is tight to within a constant factor. We also analyze a variety of pebbling algorithms, including one which achieves the 0(n/log n) bound.

Original language	English (US)
Pages (from-to)	239-251
Number of pages	13
Journal	Mathematical Systems Theory
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/BF01683275
State	Published - Dec 1976
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Mathematics
Computational Theory and Mathematics

Keywords

Pebble game
Register allocation
Space bounds
Turing machines

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10.1007/BF01683275

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AB - We study a one-person game played by placing pebbles, according to certain rules, on the vertices of a directed graph. In [3] it was shown that for each graph with n vertices and maximum in-degree d, there is a pebbling strategy which requires at most c(d) n/log n pebbles. Here we show that this bound is tight to within a constant factor. We also analyze a variety of pebbling algorithms, including one which achieves the 0(n/log n) bound.

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KW - Turing machines

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Space bounds for a game on graphs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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