{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:45:36Z","timestamp":1759063536685},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2001,12,10]],"date-time":"2001-12-10T00:00:00Z","timestamp":1007942400000},"content-version":"unspecified","delay-in-days":39,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2001,11]]},"abstract":"<jats:p>Algorithmic aspects of a chip-firing game on a graph introduced by Biggs are studied. This \nvariant of the chip-firing game, called the dollar game, has the properties that every starting \nconfiguration leads to a so-called critical configuration. The set of critical configurations \nhas many interesting properties. In this paper it is proved that the number of steps needed \nto reach a critical configuration is polynomial in the number of edges of the graph and the \nnumber of chips in the starting configuration, but not necessarily in the size of the input. \nAn alternative algorithm is also described and analysed.<\/jats:p>","DOI":"10.1017\/s0963548301004886","type":"journal-article","created":{"date-parts":[[2008,7,28]],"date-time":"2008-07-28T10:00:39Z","timestamp":1217239239000},"page":"505-529","source":"Crossref","is-referenced-by-count":10,"title":["Algorithmic Aspects of a Chip-Firing Game"],"prefix":"10.1017","volume":"10","author":[{"given":"JAN","family":"VAN DEN HEUVEL","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2001,12,10]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548301004886","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T22:23:50Z","timestamp":1557267830000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548301004886\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2001,11]]}},"alternative-id":["S0963548301004886"],"URL":"https:\/\/doi.org\/10.1017\/s0963548301004886","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,11]]}}}