{"language":[{"iso":"eng"}],"place":"Cham","date_updated":"2022-01-06T06:56:19Z","title":"An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest","publication":"International Workshop on Combinatorial Algorithms (IWOCA)","abstract":[{"lang":"eng","text":"We study the Online Prize-collecting Node-weighted Steiner Forest problem (OPC-NWSF) in which we are given an undirected graph \\(G=(V, E)\\) with \\(|V| = n\\) and node-weight function \\(w: V \\rightarrow \\mathcal {R}^+\\). A sequence of k pairs of nodes of G, each associated with a penalty, arrives online. OPC-NWSF asks to construct a subgraph H such that each pair \\(\\{s, t\\}\\) is either connected (there is a path between s and t in H) or its associated penalty is paid. The goal is to minimize the weight of H and the total penalties paid. The current best result for OPC-NWSF is a randomized \\(\\mathcal {O}(\\log ^4 n)\\)-competitive algorithm due to Hajiaghayi et al. (ICALP 2014). We improve this by proposing a randomized \\(\\mathcal {O}(\\log n \\log k)\\)-competitive algorithm for OPC-NWSF, which is optimal up to constant factor since OPC-NWSF has a randomized lower bound of \\(\\varOmega (\\log ^2 n)\\) due to Korman [11]. Moreover, our result also implies an improvement for two special cases of OPC-NWSF, the Online Prize-collecting Node-weighted Steiner Tree problem (OPC-NWST) and the Online Node-weighted Steiner Forest problem (ONWSF). In OPC-NWST, there is a distinguished node which is one of the nodes in each pair. In ONWSF, all penalties are set to infinity. The currently best known results for OPC-NWST and ONWSF are a randomized \\(\\mathcal {O}(\\log ^3 n)\\)-competitive algorithm due to Hajiaghayi et al. (ICALP 2014) and a randomized \\(\\mathcal {O}(\\log n \\log ^2 k)\\)-competitive algorithm due to Hajiaghayi et al. (FOCS 2013), respectively."}],"date_created":"2021-09-14T12:23:29Z","doi":"10.1007/978-3-319-94667-2_18","publication_status":"published","_id":"24396","status":"public","author":[{"full_name":"Markarian, Christine","last_name":"Markarian","first_name":"Christine"}],"year":"2018","user_id":"15415","publication_identifier":{"issn":["0302-9743","1611-3349"]},"type":"conference","citation":{"apa":"Markarian, C. (2018). An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest. <i>International Workshop on Combinatorial Algorithms (IWOCA)</i>. <a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">https://doi.org/10.1007/978-3-319-94667-2_18</a>","mla":"Markarian, Christine. “An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest.” <i>International Workshop on Combinatorial Algorithms (IWOCA)</i>, 2018, doi:<a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">10.1007/978-3-319-94667-2_18</a>.","chicago":"Markarian, Christine. “An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest.” In <i>International Workshop on Combinatorial Algorithms (IWOCA)</i>. Cham, 2018. <a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">https://doi.org/10.1007/978-3-319-94667-2_18</a>.","bibtex":"@inproceedings{Markarian_2018, place={Cham}, title={An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">10.1007/978-3-319-94667-2_18</a>}, booktitle={International Workshop on Combinatorial Algorithms (IWOCA)}, author={Markarian, Christine}, year={2018} }","ieee":"C. Markarian, “An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest,” 2018, doi: <a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">10.1007/978-3-319-94667-2_18</a>.","ama":"Markarian C. An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest. In: <i>International Workshop on Combinatorial Algorithms (IWOCA)</i>. ; 2018. doi:<a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">10.1007/978-3-319-94667-2_18</a>","short":"C. Markarian, in: International Workshop on Combinatorial Algorithms (IWOCA), Cham, 2018."},"department":[{"_id":"63"}]}