{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T05:22:26Z","timestamp":1768281746460,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The greedy and nearest-neighbor TSP heuristics can both have $\\log n$ approximation factors from optimal in worst case, even just for $n$ points in Euclidean space. In this note, we show that this approximation factor is only realized when the optimal tour is unusually short. In particular, for points from any fixed $d$-Ahlfor's regular metric space (which includes any $d$-manifold like the $d$-cube $[0,1]^d$ in the case $d$ is an integer but also fractals of dimension $d$ when $d$ is real-valued), our results imply that the greedy and nearest-neighbor heuristics have additive errors from optimal on the order of the optimal tour length through random points in the same space, for $d&gt;1$.<\/jats:p>","DOI":"10.37236\/12651","type":"journal-article","created":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T15:45:23Z","timestamp":1727970323000},"source":"Crossref","is-referenced-by-count":3,"title":["The Bright Side of Simple Heuristics for the TSP"],"prefix":"10.37236","volume":"31","author":[{"given":"Alan","family":"Frieze","sequence":"first","affiliation":[]},{"given":"Wesley","family":"Pegden","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2024,10,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T15:45:23Z","timestamp":1727970323000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i4p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,4]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12651","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,4]]},"article-number":"P4.5"}}