{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:26:46Z","timestamp":1787336806217,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We consider the problem of embedding weighted hyperedges of a hypergraph as paths in a cycle on the same number of vertices, such that the maximum congestion of any physical link of the cycle is minimized. The problem, called weighted hypergraph embedding in a cycle (WHEC), is known to be NP-complete even when each hyperedge is unweighted or each weighted hyperedge contains exactly two vertices. In this paper, we propose an improved rounding algorithm for the WHEC problem to provide a solution with an approximation bound of $1.5(opt+w_{max})$, where $opt$ represents the optimal value of the problem and $w_{max}$ denotes the largest weight of hyperedges. For any fixed $\\varepsilon &gt; 0$, we also present a polynomial time algorithm to provide an embedding whose congestion is at most $(1.5+\\varepsilon)$ times the optimum. This improves previous results for the general WHEC problem.<\/jats:p>","DOI":"10.1137\/050631951","type":"journal-article","created":{"date-parts":[[2008,1,22]],"date-time":"2008-01-22T15:51:56Z","timestamp":1201017116000},"page":"1490-1500","source":"Crossref","is-referenced-by-count":3,"title":["Improved Approximation Algorithms for Weighted Hypergraph Embedding in a Cycle"],"prefix":"10.1137","volume":"18","author":[{"given":"Hann-Jang","family":"Ho","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"SingLing","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,1,16]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(03)00297-7"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1145\/48014.48018"},{"key":"R3","unstructured":"J. L. Ganley and J. P. Cohoon,\n                      A provably good moat routing algorithm\n                      , in Proceedings of the 6th Great Lakes Symposium on VLSI, IEEE Computer Society, Washington, DC, 1996, pp. 86\u201391."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(92)90007-W"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1109\/12.589233"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(98)00117-3"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1109\/12.736445"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2006.34"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2005.62"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"X. Deng and G. Li,\n                      A PTAS for embedding hypergraph in a cycle (extended abstract)\n                      , in Proceedings of the 31st International Colloquium on Automata, Languages and Programming (Turku, Finland, 2004), Springer, Berlin, 2004, pp. 433\u2013444.","DOI":"10.1007\/978-3-540-27836-8_38"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02110141"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480195294994"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1002\/bltj.2047"},{"key":"R14","unstructured":"G. Wilfong and P. Winkler,\n                      Ring routing and wavelength translation\n                      , in Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, 1998, pp. 333\u2013341."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480199358709"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"S. Vempala and B. V\u00f6cking,\n                      Approximating multicast congestion\n                      , in Proceedings of the 10th International Symposium on Algorithms and Computation, Springer, Berlin, 1999, pp. 367\u2013372.","DOI":"10.1007\/3-540-46632-0_37"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"R. Carr and S. Vempala,\n                      Randomized metarounding\n                      , in Proceedings of the 32nd ACM Symposium on Theory of Computing, 2000, pp. 58\u201362.","DOI":"10.1145\/335305.335312"},{"key":"R18","unstructured":"K. Jansen and H. Zhang,\n                      An approximation algorithm for the multicast congestion problem via minimum Steiner trees\n                      , in Proceedings of the 3rd International Workshop on Approximation and Randomized Algorithms in Communication Networks, Carleton Scientific, Waterloo, ON, Canada, 2002, pp. 1\u201315."}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050631951","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:31:33Z","timestamp":1787333493000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050631951"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/050631951"],"URL":"https:\/\/doi.org\/10.1137\/050631951","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}