{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86805"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86805","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Equitable List Coloring, Induced Linear Forests, and Routing in Rooted Graphs","abstract":"We explicitly characterize the family of networks for which such a protocol exists. This characterization is given in terms of forbidden rooted minors, which leads to a linear time recognition algorithm for this family of networks. We obtain a similar characterization for the family of networks in which a message can be broadcast from a single node s to all other nodes. Finally, we show that there is a forbidden rooted minor characterization for the more general case when a header (containing routing information) of fixed length is attached to the message, and we discuss the algorithmic consequences of this characterization.","abstract_html":"We explicitly characterize the family of networks for which such a protocol exists. This characterization is given in terms of forbidden rooted minors, which leads to a linear time recognition algorithm for this family of networks. We obtain a similar characterization for the family of networks in which a message can be broadcast from a single node s to all other nodes. 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This characterization is given in terms of forbidden rooted minors, which leads to a linear time recognition algorithm for this family of networks. We obtain a similar characterization for the family of networks in which a message can be broadcast from a single node s to all other nodes. Finally, we show that there is a forbidden rooted minor characterization for the more general case when a header (containing routing information) of fixed length is attached to the message, and we discuss the algorithmic consequences of this characterization.","Made available in DSpace on 2015-09-28T15:19:37Z (GMT). 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This characterization is given in terms of forbidden rooted minors, which leads to a linear time recognition algorithm for this family of networks. We obtain a similar characterization for the family of networks in which a message can be broadcast from a single node s to all other nodes. Finally, we show that there is a forbidden rooted minor characterization for the more general case when a header (containing routing information) of fixed length is attached to the message, and we discuss the algorithmic consequences of this characterization.","Made available in DSpace on 2015-09-28T15:19:37Z (GMT). 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