A comparison of two variations of a pebble game on graphs
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TLDR
The number of pebbles used in the black [black-white] pebble game corresponds to the storage requirement of the deterministic [non-deterministic] evaluation of a straight line program.About:
This article is published in Theoretical Computer Science.The article was published on 1981-01-01 and is currently open access. It has received 45 citations till now. The article focuses on the topics: Vertex (graph theory) & Directed acyclic graph.read more
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Searching and pebbling
TL;DR: In this article, the search number of an undirected graph G with the minimum and maximum of the progressive pebble demands of the directed acyclic graphs obtained by orienting G was derived.
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Min cut is NP-complete for edge weighted trees
TL;DR: The Min Cut Linear Arrangement Problem is NP-complete for trees with polynomial size edge weights and this is used to show the NP-completeness of Search Number, Vertex Separation, Progressive Black/White Pebble Demand, and Topological Bandwidth for planar graphs with maximum vertex degree 3.
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A polynomial algorithm for the min-cut linear arrangement of trees
TL;DR: An algorithm is presented which finds a min-cut linear arrangement of a tree in O(nlogn) time and an extension of the algorithm determines the number of pebbles needed to play the black and white pebble game on a tree.
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Combinatorial games: Selected bibliography with a succinct gourmet introduction.
TL;DR: The family of combinatorial games consists of two-player games with perfect information, no hidden information as in some card games, no chance moves and outcome restricted to (lose, win), (tie, tie) and (draw, draw) for the two players who move alternately.
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Black-white pebbles and graph separation
TL;DR: It is shown that instances of the black-white pebble game and the vertex separator game can easily be transformed into each other and both games are shown to be NP-complete.
References
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On Time Versus Space
TL;DR: The context-sensitive languages cannot be recognized in linear time by deterministic multitape Turing machines, and are strictly contained in the class of languages recognized by Turing machines of tape complexity.
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An observation on time-storage trade off
TL;DR: There are two main results proved here that state that a certain set SP of strings (those coding ''solvable path systems'') has tape complexity (log n)^2 iff every set in (i.e., of deterministic polynomial time complexity) has Tape complexity ( log n,^2).
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Space bounds for a game on graphs
TL;DR: It is shown that for each graph withn vertices and maximum in-degreed, there is a pebbling strategy which requires at mostc(d) n/logn pebbles, and this bound is tight to within a constant factor.
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Storage requirements for deterministic polynomialtime recognizable languages
Stephen A. Cook,Ravi Sethi +1 more
TL;DR: This paper presents further evidence in support of the conjecture that SP cannot be recognized using storage (log n)^k for any k, and proves the result for a suitably restricted device.
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The space complexity of pebble games on trees
Thomas Lengauer,Robert E. Tarjan +1 more
TL;DR: Two different pebble games that are yed on directed ‘acyclic graphs’ that are studied in the past and one game uses ek pebbles only and is called the black pebbling game.