Time-space trade-offs in a pebble game

W. J. Paul; R. E. Tarjan

doi:10.1007/BF00289150

Time-space trade-offs in a pebble game

W. J. Paul
, R. E. Tarjan

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

24 Scopus citations

Abstract

A certain pebble game on graphs has been studied in various contexts as a model for the time and space requirements of computations [1,2,3,8]. In this note it is shown that there exists a family of directed acyclic graphs G_n and constants c₁, c₂, c₃ such that (1) G_n has n nodes and each node in G_n has indegree at most 2. (2) Each graph G_n can be pebbled with c₁√n pebbles in n moves. (3) Each graph G_n can also be pebbled with c₂√n pebbles, c₂<c₁, but every strategy which achieves this has at least 2^c₃√n moves.

Original language	English (US)
Pages (from-to)	111-115
Number of pages	5
Journal	Acta Informatica
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/BF00289150
State	Published - Jun 1978
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
Information Systems
Computer Networks and Communications

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10.1007/BF00289150

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abstract = "A certain pebble game on graphs has been studied in various contexts as a model for the time and space requirements of computations [1,2,3,8]. In this note it is shown that there exists a family of directed acyclic graphs Gn and constants c1, c2, c3 such that (1) Gn has n nodes and each node in Gn has indegree at most 2. (2) Each graph Gn can be pebbled with c1√n pebbles in n moves. (3) Each graph Gn can also be pebbled with c2√n pebbles, c21, but every strategy which achieves this has at least 2c3√n moves.",

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AU - Tarjan, R. E.

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AB - A certain pebble game on graphs has been studied in various contexts as a model for the time and space requirements of computations [1,2,3,8]. In this note it is shown that there exists a family of directed acyclic graphs Gn and constants c1, c2, c3 such that (1) Gn has n nodes and each node in Gn has indegree at most 2. (2) Each graph Gn can be pebbled with c1√n pebbles in n moves. (3) Each graph Gn can also be pebbled with c2√n pebbles, c21, but every strategy which achieves this has at least 2c3√n moves.

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Time-space trade-offs in a pebble game

Abstract

All Science Journal Classification (ASJC) codes

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