منابع مشابه
Planar graph is on fire
Let G be any connected graph on n vertices, n ≥ 2. Let k be any positive integer. Suppose that a fire breaks out on some vertex of G. Then in each turn k firefighters can protect vertices of G — each can protect one vertex not yet on fire; Next a fire spreads to all unprotected neighbours. The k-surviving rate of G, denoted by ρ k (G), is the expected fraction of vertices that can be saved from...
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Is perfect matching in NC? That is to say, is there a deterministic fast parallel algorithm for it? This has been an outstanding open question in theoretical computer science for over three decades, ever since the discovery of RNC matching algorithms. Within this question, the case of planar graphs has remained an enigma: On the one hand, counting the number of perfect matchings is far harder t...
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We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. We present positive and negative results for the two versions of the problem. Among the positive results with given mapping, we show that we can embed two paths on an n×...
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We present a dynamic data structure for the incremental construction of a planar embedding of a planar graph. The data structure supports the following Ž . operations: i testing if a new edge can be added to the embedding without Ž . introducing crossing; and ii adding vertices and edges. The time complexity of Ž . Ž . each operation is O log n amortized for edge insertion , and the memory spac...
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Approximation algorithms for a class of planar graph problems, including planar independent set, planar vertex cover and planar dominating set, were intensively studied. The current upper bound on the running time of the polynomial time approximation schemes (PTAS) for these planar graph problems is of 2 n. Here we study the lower bound on the running time of the PTAS for these planar graph pro...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2015
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.06.002