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Separator-based graph embedding into multidimensional grids with small edge-congestion
http://hdl.handle.net/2297/40596
http://hdl.handle.net/2297/405962e306ac7-a161-4453-8294-8bf43b187955
名前 / ファイル | ライセンス | アクション |
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TE-PR-MATSUBAYASHI-A-119.pdf (267.8 kB)
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2017-10-03 | |||||
タイトル | ||||||
タイトル | Separator-based graph embedding into multidimensional grids with small edge-congestion | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | journal article | |||||
著者 |
Matsubayashi, Akira
× Matsubayashi, Akira |
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書誌情報 |
Discrete Applied Mathematics 巻 185, p. 119-137, 発行日 2015-04-20 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0166-218X | |||||
NCID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA00161253 | |||||
DOI | ||||||
関連タイプ | isVersionOf | |||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1016/j.dam.2014.11.024 | |||||
出版者 | ||||||
出版者 | Elsevier | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We study the problem of embedding a guest graph with minimum edge-congestion into a multidimensional grid with the same size as that of the guest graph. Based on a well-known notion of graph separators, we show that an embedding with a smaller edge-congestion can be obtained if the guest graph has a smaller separator, and if the host grid has a higher but constant dimension. Specifically, we prove that any graph with NN nodes, maximum node degree ΔΔ, and with a node-separator of size ss, where ss is a function such that s(n)=O(nα)s(n)=O(nα) with 0≤α<10≤α<1, can be embedded into a grid of a fixed dimension d≥2d≥2 with at least NN nodes, with an edge-congestion of O(Δ)O(Δ) if d>1/(1−α)d>1/(1−α), O(ΔlogN)O(ΔlogN) if d=1/(1−α)d=1/(1−α), and View the MathML sourceO(ΔNα−1+1d) if d<1/(1−α)d<1/(1−α). This edge-congestion achieves constant ratio approximation if d>1/(1−α)d>1/(1−α), and matches an existential lower bound within a constant factor if d≤1/(1−α)d≤1/(1−α). Our result implies that if the guest graph has an excluded minor of a fixed size, such as a planar graph, then we can obtain an edge-congestion of O(ΔlogN)O(ΔlogN) for d=2d=2 and O(Δ)O(Δ) for any fixed d≥3d≥3. Moreover, if the guest graph has a fixed treewidth, such as a tree, an outerplanar graph, and a series–parallel graph, then we can obtain an edge-congestion of O(Δ)O(Δ) for any fixed d≥2d≥2. To design our embedding algorithm, we introduce edge-separators bounding extension , such that in partitioning a graph into isolated nodes using edge-separators recursively, the number of outgoing edges from a subgraph to be partitioned in a recursive step is bounded. We present an algorithm to construct an edge-separator with extension of O(Δnα)O(Δnα) from a node-separator of size O(nα)O(nα). | |||||
著者版フラグ | ||||||
出版タイプ | AM | |||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa |