{"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1612.03856","open_access":"1"}],"title":"Improved algorithms for decremental single-source reachability on directed graphs","quality_controlled":"1","scopus_import":"1","intvolume":"      9134","language":[{"iso":"eng"}],"date_published":"2015-01-01T00:00:00Z","publisher":"Springer Nature","year":"2015","day":"01","publication":"42nd International Colloquium on Automata, Languages and Programming","publication_status":"published","abstract":[{"text":"Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with 𝑜(𝑚𝑛) total update time, where 𝑚 is the number of edges and 𝑛 is the number of nodes in the graph [Henzinger et al. STOC 2014]. The algorithm is a combination of several different algorithms, each for a different 𝑚 vs. 𝑛 trade-off. For the case of 𝑚=Θ(𝑛1.5) the running time is 𝑂(𝑛2.47), just barely below 𝑚𝑛=Θ(𝑛2.5). In this paper we simplify the previous algorithm using new algorithmic ideas and achieve an improved running time of 𝑂̃ (min(𝑚7/6𝑛2/3,𝑚3/4𝑛5/4+𝑜(1),𝑚2/3𝑛4/3+𝑜(1)+𝑚3/7𝑛12/7+𝑜(1))). This gives, e.g., 𝑂(𝑛2.36) for the notorious case 𝑚=Θ(𝑛1.5). We obtain the same upper bounds for the problem of maintaining the strongly connected components of a directed graph undergoing edge deletions. Our algorithms are correct with high probabililty against an oblivious adversary.","lang":"eng"}],"doi":"10.1007/978-3-662-47672-7_59","author":[{"first_name":"Monika H","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"Sebastian","full_name":"Krinninger, Sebastian","last_name":"Krinninger"},{"last_name":"Nanongkai","full_name":"Nanongkai, Danupon","first_name":"Danupon"}],"conference":{"start_date":"2015-07-06","end_date":"2015-07-10","name":"ICALP: International Colloquium on Automata, Languages, and Programming","location":"Kyoto, Japan"},"_id":"11785","alternative_title":["LNCS"],"publication_identifier":{"issn":["0302-9743"],"isbn":["9783662476710"]},"volume":9134,"date_updated":"2023-02-10T09:10:26Z","type":"conference","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"page":"725 - 736","status":"public","external_id":{"arxiv":["1612.03856"]},"citation":{"ieee":"M. H. Henzinger, S. Krinninger, and D. Nanongkai, “Improved algorithms for decremental single-source reachability on directed graphs,” in <i>42nd International Colloquium on Automata, Languages and Programming</i>, Kyoto, Japan, 2015, vol. 9134, pp. 725–736.","ama":"Henzinger MH, Krinninger S, Nanongkai D. Improved algorithms for decremental single-source reachability on directed graphs. In: <i>42nd International Colloquium on Automata, Languages and Programming</i>. Vol 9134. Springer Nature; 2015:725-736. doi:<a href=\"https://doi.org/10.1007/978-3-662-47672-7_59\">10.1007/978-3-662-47672-7_59</a>","mla":"Henzinger, Monika H., et al. “Improved Algorithms for Decremental Single-Source Reachability on Directed Graphs.” <i>42nd International Colloquium on Automata, Languages and Programming</i>, vol. 9134, Springer Nature, 2015, pp. 725–36, doi:<a href=\"https://doi.org/10.1007/978-3-662-47672-7_59\">10.1007/978-3-662-47672-7_59</a>.","short":"M.H. Henzinger, S. Krinninger, D. Nanongkai, in:, 42nd International Colloquium on Automata, Languages and Programming, Springer Nature, 2015, pp. 725–736.","apa":"Henzinger, M. H., Krinninger, S., &#38; Nanongkai, D. (2015). Improved algorithms for decremental single-source reachability on directed graphs. In <i>42nd International Colloquium on Automata, Languages and Programming</i> (Vol. 9134, pp. 725–736). Kyoto, Japan: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-662-47672-7_59\">https://doi.org/10.1007/978-3-662-47672-7_59</a>","chicago":"Henzinger, Monika H, Sebastian Krinninger, and Danupon Nanongkai. “Improved Algorithms for Decremental Single-Source Reachability on Directed Graphs.” In <i>42nd International Colloquium on Automata, Languages and Programming</i>, 9134:725–36. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/978-3-662-47672-7_59\">https://doi.org/10.1007/978-3-662-47672-7_59</a>.","ista":"Henzinger MH, Krinninger S, Nanongkai D. 2015. Improved algorithms for decremental single-source reachability on directed graphs. 42nd International Colloquium on Automata, Languages and Programming. ICALP: International Colloquium on Automata, Languages, and Programming, LNCS, vol. 9134, 725–736."},"date_created":"2022-08-11T08:51:32Z","month":"01","article_processing_charge":"No"}