{"created":"2023-07-27T06:25:26.680630+00:00","id":8743,"links":{},"metadata":{"_buckets":{"deposit":"ee397308-7dc8-4d59-8f84-79dfe7a63c59"},"_deposit":{"created_by":3,"id":"8743","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"8743"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00008743","sets":["934:935:936"]},"author_link":["614"],"item_4_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2015-04-20","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"137","bibliographicPageStart":"119","bibliographicVolumeNumber":"185","bibliographic_titles":[{"bibliographic_title":"Discrete Applied Mathematics"}]}]},"item_4_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"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).","subitem_description_type":"Abstract"}]},"item_4_publisher_17":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Elsevier"}]},"item_4_relation_12":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type":"isVersionOf","subitem_relation_type_id":{"subitem_relation_type_id_text":"10.1016/j.dam.2014.11.024","subitem_relation_type_select":"DOI"}}]},"item_4_source_id_11":{"attribute_name":"NCID","attribute_value_mlt":[{"subitem_source_identifier":"AA00161253","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0166-218X","subitem_source_identifier_type":"ISSN"}]},"item_4_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Matsubayashi, Akira"}],"nameIdentifiers":[{},{},{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-10-03"}],"displaytype":"detail","filename":"TE-PR-MATSUBAYASHI-A-119.pdf","filesize":[{"value":"267.8 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"TE-PR-MATSUBAYASHI-A-119.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/8743/files/TE-PR-MATSUBAYASHI-A-119.pdf"},"version_id":"da035f46-42a2-4bf0-adee-a1624796bebe"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"journal article","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Separator-based graph embedding into multidimensional grids with small edge-congestion","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Separator-based graph embedding into multidimensional grids with small edge-congestion"}]},"item_type_id":"4","owner":"3","path":["936"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-03"},"publish_date":"2017-10-03","publish_status":"0","recid":"8743","relation_version_is_last":true,"title":["Separator-based graph embedding into multidimensional grids with small edge-congestion"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-07-28T02:04:27.506572+00:00"}