| 講演名 | 2013/10/30 Bounding Dilation of Separator-Based Graph Embeddings into Grids , |
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| PDFダウンロードページ | PDFダウンロードページへ |
| 抄録(和) | |
| 抄録(英) | In this report, we address a classical problem of embedding a guest graph with minimum dilation into a multidimensional grid of the same size as that of the guest graph, and propose a relatively simple embedding bounding dilation based on graph separators. Specifically, we prove that any graph with N nodes, maximum node degree Δ≥2, and with a node-separator of size O(n^α) can be embedded with a dilation of O(N^<1/d>logΔ/log N) into a grid of a fixed dimension d≥2 with at least N nodes, where α is a fixed number with 0≤α<1. This dilation matches a trivial lower bound within a constant factor. A remarkable merit of the proposed embedding is that it can be used to bound the dilation of another embedding algorithm. Combining the proposed embedding with a previous embedding algorithm bounding the edge-congestion, we can obtain an edge-congestion of O(Δ) as well as the dilation O(N^<1/d>logΔ/log N) if d>1/(1-α). This congestion achieves constant ratio approximation. For d≤1/(1-α), we present a trade-off between tight upper bounds of dilation and edge-congestion. Specifically, we prove a dilation of O((N^<1/d>logΔ)/(εlog N)) and an edge-congestion of O(Δ(N^<α-1+1/d+ε)+log N)) for any 1/log N≤ε<1-α. These dilation and edge-congestion match existential lower bounds within a constant factor for ε=Ω(1) and ε=1/log N, respectively. Besides, there exists a guest graph for which better dilation and edge-congestion cannot be obtained for ε=log log N/log N. The above results improve and generalize a number of previous results. |
| キーワード(和) | |
| キーワード(英) | graph embedding / dilation / congestion / grid / separator |
| 資料番号 | Vol.2013-AL-145 No.18 |
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| 研究会情報 | |
| 研究会 | MSS |
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| 開催期間 | 2013/10/30(から1日開催) |
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| 講演論文情報詳細 | |
| 申込み研究会 | Mathematical Systems Science and its applications(MSS) |
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| 本文の言語 | ENG |
| タイトル（和） | |
| サブタイトル（和） | |
| タイトル（英） | Bounding Dilation of Separator-Based Graph Embeddings into Grids |
| サブタイトル（和） | |
| キーワード(1)（和/英） | / graph embedding |
| 第 1 著者 氏名（和/英） | / AKIRA MATSUBAYASHI |
| 第 1 著者 所属（和/英） | Division of Electrical Engineering and Computer Science, Kanazawa University |
| 発表年月日 | 2013/10/30 |
| 資料番号 | Vol.2013-AL-145 No.18 |
| 巻番号（vol） | vol.113 |
| 号番号（no） | 279 |
| ページ範囲 | pp.- |
| ページ数 | 8 |
| 発行日 | |