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On the weighted ▫$k$▫-path vertex cover problemBrešar, Boštjan ...Podmnožica ▫$S$▫ množice vozlišč grafa ▫$G$▫ se imenuje vozliščno pokritje ▫$k$▫-poti, če vsaka pot reda ▫$k$▫ v ▫$G$▫ vsebuje vsaj eno vozlišče iz ▫$S$▫. Kardinalnost najmanjšega vozliščnega ... pokritja ▫$k$▫-poti se imenuje število vozliščnega pokritja ▫$k$▫-poti grafa ▫$G$▫ in ga označimo z ▫$\psi_k(G)$▫. Znano je, da je problem najmanjšega vozliščnega pokritja ▫$k$▫-poti (▫$k$▫-PVCP) NP-poln za vse ▫$k \ge 2$▫. V tem članku obravnavamo uteženo verzijo problema ▫$k$▫-PVCP (▫$k$▫-WPVCP), v kateri so vozlišča utežena, problem pa je poiskati takšno množico z najmanjšo skupno težo v grafu ▫$G$▫, po odstranitvi te množice iz grafa ▫$G$▫ v grafu ne ostane nobena pot ▫$P_k$▫. Problem sta na kratko vpeljala že Tu in Thou (2011), vendar doslej še ni bil podrobneje obravnavan. Predstavimo rešitve in učinkovite algoritme za problem ▫$k$▫-WPVCP v nekaterih posebnih razredih grafov. To naredimo za polne grafe in cikle ter kot najpomembnejši rezultat predstavimo algoritem, ki izračuna število vozliščnega pokritja ▫$k$▫-poti na poljubnem uteženem drevesu s časovno zahtevnostjo ▫$O(k \cdot |V(G)|)$▫.Source: Discrete applied mathematics. - ISSN 0166-218X (Vol. 177, 2014, str. 14-18)Type of material - article, component part ; adult, seriousPublish date - 2014Language - englishCOBISS.SI-ID - 7331347
Author
Brešar, Boštjan |
Krivoš-Belluš, Rastislav |
Semanišin, Gabriel |
Šparl, Petra, 1975-2016
Topics
uteženi graf |
vozliščno pokritje |
drevo |
grafovski algoritem |
weighted graph |
vertex cover |
tree |
graph algorithm
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Brešar, Boštjan | 17005 |
Krivoš-Belluš, Rastislav | ![]() |
Semanišin, Gabriel | ![]() |
Šparl, Petra, 1975-2016 | 20495 |
Source: Personal bibliographies
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