{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:08Z","timestamp":1753893848619,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We introduce a technique using linear programming that may be used to analyse the worst-case performance of a class of greedy heuristics for certain optimisation problems on regular graphs. We demonstrate the use of this technique on heuristics for bounding the size of a minimum maximal matching (MMM), a minimum connected dominating set (MCDS) and a minimum independent dominating set (MIDS) in cubic graphs. We show that for $n$-vertex connected cubic graphs, the size of an MMM is at most $9n\/20+O(1)$, which is a new result. We also show that the size of an MCDS is at most $3n\/4+O(1)$ and the size of a MIDS is at most $29n\/70+O(1)$. These results are not new, but earlier proofs involved rather long ad-hoc arguments. By contrast, our method is to a large extent automatic and can apply to other problems as well. We also consider $n$-vertex connected cubic graphs of girth at least 5 and for such graphs we show that the size of an MMM is at most $3n\/7+O(1)$, the size of an MCDS is at most $2n\/3+O(1)$ and the size of a MIDS is at most $3n\/8+O(1)$.<\/jats:p>","DOI":"10.37236\/449","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:58:32Z","timestamp":1578715112000},"source":"Crossref","is-referenced-by-count":3,"title":["Linear Programming and the Worst-Case Analysis of Greedy Algorithms on Cubic Graphs"],"prefix":"10.37236","volume":"17","author":[{"given":"W.","family":"Duckworth","sequence":"first","affiliation":[]},{"given":"N.","family":"Wormald","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,12,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r177\/appendix","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r177\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:18:47Z","timestamp":1579303127000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r177"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/449","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,12,10]]},"article-number":"R177"}}