{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:40:41Z","timestamp":1787337641538,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>\n                    A layered graph is a connected graph whose vertices are partitioned into sets L\n                    <jats:sub>0<\/jats:sub>\n                    =s, L\n                    <jats:sub>1<\/jats:sub>\n                    , L\n                    <jats:sub>2<\/jats:sub>\n                    ,..., and whose edges, which have nonnegative integral weights, run between consecutive layers. Its width is $\\max\\{|L_i|\\}$. In the on-line layered graph traversal problem, a searcher starts at s in a layered graph of unknown width and tries to reach a target vertex t; however, the vertices in layer i and the edges between layers i-1 and i are only revealed when the searcher reaches layer i-1.\n                  <\/jats:p>\n                  <jats:p>\n                    We give upper and lower bounds on the competitive ratio of layered graph traversal algorithms. We give a deterministic on-line algorithm which is O(9\n                    <jats:sup>w<\/jats:sup>\n                    )-competitive on width-w graphs and prove that for no w can a deterministic on-line algorithm have a competitive ratio better than 2\n                    <jats:sup>w-2<\/jats:sup>\n                    on width-w graphs. We prove that for all w, w\/2 is a lower bound on the competitive ratio of any randomized on-line layered graph traversal algorithm. For traversing layered graphs consisting of w disjoint paths tied together at a common source, we give a randomized on-line algorithm with a competitive ratio of O(log w) and prove that this is optimal up to a constant factor.\n                  <\/jats:p>","DOI":"10.1137\/s0097539795279943","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"447-462","source":"Crossref","is-referenced-by-count":14,"title":["Competitive Algorithms for Layered Graph Traversal"],"prefix":"10.1137","volume":"28","author":[{"given":"Amos","family":"Fiat","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dean P.","family":"Foster","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Howard","family":"Karloff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuval","family":"Rabani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiftach","family":"Ravid","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sundar","family":"Vishwanathan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1145\/77600.77615"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1993.1054"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/102435"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01294260"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1145\/146585.146588"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1996.0024"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1145\/174130.174131"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"Marek Chrobak, Lawrence Larmore, The server problem and on\u2010line games, DIMACS Ser. 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