{"id":{"repo_id":"brazil-uerj","oai_identifier":"oai:pantheon.ufrj.br:11422/8166"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-uerj/oai:pantheon.ufrj.br:11422/8166","repository":{"repo_id":"brazil-uerj","name":"Brazil UERJ","base_url":"https://pantheon.ufrj.br/oai/request"},"display":{"title":"Conexão de terminais com limitação de roteadores: complexidade e relação com fluxos e caminhos disjuntos","abstract":"A connection tree of a graph G for a non-empty subset W ⊆ V (G) is a tree subgraph of G such that W ⊆ V (T) and every leaf of T belongs to W. The vertices in W are called terminals, the vertices in V (T) \\ W with degree 2 in T are called linkers and the vertices in V (T) \\ W with degree at least 3 in T are called routers. In 2012, Dourado et al. proposed the Terminal connection problem (TCP), which consists in the following question: “given a connected graph G, a terminal set W and two non-negative integers ` and r; does G admit a connection tree for W such that it has at most ` linkers and at most r routers? ”. The TCP was proved to be NP-complete even when either ` or r is bounded by a constant; conversely, the problem was proved to be polynomial-time solvable if ` and r are both bounded by constants. Later, in 2014, Dourado et al. proposed the strict variant of the TCP which further requires that every terminal must be a leaf of T, and it is denoted by S-TCP. As the TCP, the S-TCP was proved to be NP-complete if ` is bounded by a constant and be polynomial-time solvable if ` and r are both bounded by constants; however, the case in which just r is bounded by a constant was not considered. Thus, we study in this dissertation the S-TCP restricted to the case in which r is bounded by a constant. More specifically, we provide a polynomial-time algorithm for the S-TCP when r ∈ {0, 1} and we prove partial results for the case r ≥ 2, exposing relations with network flows and disjoint paths. Moreover, we determine the complexity of some variants of the S-TCP. Lastly, we study the S-TCP and the TCP when the maximum degree of the graph G is bounded.","abstract_html":"A connection tree of a graph G for a non-empty subset W ⊆ V (G) is a tree subgraph of G such that W ⊆ V (T) and every leaf of T belongs to W. The vertices in W are called terminals, the vertices in V (T) \\ W with degree 2 in T are called linkers and the vertices in V (T) \\ W with degree at least 3 in T are called routers. In 2012, Dourado et al. proposed the Terminal connection problem (TCP), which consists in the following question: “given a connected graph G, a terminal set W and two non-negative integers ` and r; does G admit a connection tree for W such that it has at most ` linkers and at most r routers? ”. The TCP was proved to be NP-complete even when either ` or r is bounded by a constant; conversely, the problem was proved to be polynomial-time solvable if ` and r are both bounded by constants. Later, in 2014, Dourado et al. proposed the strict variant of the TCP which further requires that every terminal must be a leaf of T, and it is denoted by S-TCP. As the TCP, the S-TCP was proved to be NP-complete if ` is bounded by a constant and be polynomial-time solvable if ` and r are both bounded by constants; however, the case in which just r is bounded by a constant was not considered. Thus, we study in this dissertation the S-TCP restricted to the case in which r is bounded by a constant. More specifically, we provide a polynomial-time algorithm for the S-TCP when r ∈ {0, 1} and we prove partial results for the case r ≥ 2, exposing relations with network flows and disjoint paths. Moreover, we determine the complexity of some variants of the S-TCP. Lastly, we study the S-TCP and the TCP when the maximum degree of the graph G is bounded.","abstract_has_math":false,"creators":["Melo, Alexsander Andrade de"],"institution":"Universidade Federal do Rio de Janeiro","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Figueiredo, Celina Miraglia Herrera de"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-02","date_published":"2017-02","updated_at":"2026-07-24T01:16:29Z","subjects":["Conexões de terminais","Caminhos disjuntos"],"languages":["por"],"rights":["Acesso Aberto"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11422/8166","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Figueiredo, Celina Miraglia Herrera de"]},{"key":"dc:creator","label":"Author","values":["Melo, Alexsander Andrade de"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-05-23T15:42:49Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-16T03:05:41Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-02"]},{"key":"dc:publisher","label":"Institution","values":["Universidade Federal do Rio de Janeiro"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"]},{"key":"dc:type","label":"Dc Type","values":["Dissertação"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Conexões de terminais","Caminhos disjuntos"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["por"]},{"key":"dc:rights","label":"Dc Rights","values":["Acesso Aberto"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11422/8166"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A connection tree of a graph G for a non-empty subset W ⊆ V (G) is a tree subgraph of G such that W ⊆ V (T) and every leaf of T belongs to W. The vertices in W are called terminals, the vertices in V (T) \\ W with degree 2 in T are called linkers and the vertices in V (T) \\ W with degree at least 3 in T are called routers. In 2012, Dourado et al. proposed the Terminal connection problem (TCP), which consists in the following question: “given a connected graph G, a terminal set W and two non-negative integers ` and r; does G admit a connection tree for W such that it has at most ` linkers and at most r routers? ”. The TCP was proved to be NP-complete even when either ` or r is bounded by a constant; conversely, the problem was proved to be polynomial-time solvable if ` and r are both bounded by constants. Later, in 2014, Dourado et al. proposed the strict variant of the TCP which further requires that every terminal must be a leaf of T, and it is denoted by S-TCP. As the TCP, the S-TCP was proved to be NP-complete if ` is bounded by a constant and be polynomial-time solvable if ` and r are both bounded by constants; however, the case in which just r is bounded by a constant was not considered. Thus, we study in this dissertation the S-TCP restricted to the case in which r is bounded by a constant. More specifically, we provide a polynomial-time algorithm for the S-TCP when r ∈ {0, 1} and we prove partial results for the case r ≥ 2, exposing relations with network flows and disjoint paths. Moreover, we determine the complexity of some variants of the S-TCP. Lastly, we study the S-TCP and the TCP when the maximum degree of the graph G is bounded."]},{"key":"dc:title","label":"Title","values":["Conexão de terminais com limitação de roteadores: complexidade e relação com fluxos e caminhos disjuntos"]}]}],"canonical_facts":{"dc:contributor.advisor":["Figueiredo, Celina Miraglia Herrera de"],"dc:creator":["Melo, Alexsander Andrade de"],"dc:date.accessioned":["2019-05-23T15:42:49Z"],"dc:date.available":["2026-05-16T03:05:41Z"],"dc:date.issued":["2017-02"],"dc:description.abstract":["A connection tree of a graph G for a non-empty subset W ⊆ V (G) is a tree subgraph of G such that W ⊆ V (T) and every leaf of T belongs to W. The vertices in W are called terminals, the vertices in V (T) \\ W with degree 2 in T are called linkers and the vertices in V (T) \\ W with degree at least 3 in T are called routers. In 2012, Dourado et al. proposed the Terminal connection problem (TCP), which consists in the following question: “given a connected graph G, a terminal set W and two non-negative integers ` and r; does G admit a connection tree for W such that it has at most ` linkers and at most r routers? ”. The TCP was proved to be NP-complete even when either ` or r is bounded by a constant; conversely, the problem was proved to be polynomial-time solvable if ` and r are both bounded by constants. Later, in 2014, Dourado et al. proposed the strict variant of the TCP which further requires that every terminal must be a leaf of T, and it is denoted by S-TCP. As the TCP, the S-TCP was proved to be NP-complete if ` is bounded by a constant and be polynomial-time solvable if ` and r are both bounded by constants; however, the case in which just r is bounded by a constant was not considered. Thus, we study in this dissertation the S-TCP restricted to the case in which r is bounded by a constant. More specifically, we provide a polynomial-time algorithm for the S-TCP when r ∈ {0, 1} and we prove partial results for the case r ≥ 2, exposing relations with network flows and disjoint paths. Moreover, we determine the complexity of some variants of the S-TCP. Lastly, we study the S-TCP and the TCP when the maximum degree of the graph G is bounded."],"dc:identifier.uri":["http://hdl.handle.net/11422/8166"],"dc:language":["por"],"dc:publisher":["Universidade Federal do Rio de Janeiro"],"dc:publisher.department":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"],"dc:rights":["Acesso Aberto"],"dc:subject":["Conexões de terminais","Caminhos disjuntos"],"dc:title":["Conexão de terminais com limitação de roteadores: complexidade e relação com fluxos e caminhos disjuntos"],"dc:type":["Dissertação"]},"updated_at":"2026-07-24T01:16:29Z"}