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Given an undirected unweighted graph, the almost minimum cycle is defined as the cycle whose length is greater than that of a minimum cycle by at most one. Itai and Rodeh in a seminal paper in 1978 gave a simple O(n^2) algorithm to find such an almost minimum cycle. My question is, has it been improved ever since? If yes, which paper does that?

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  • $\begingroup$ For the lazy, here's a Google-Scholar link to the paper. Here's a link to the papers that cite that one. As of August 2018, Google Scholar returns only four papers that cite that one and contain the phrase "Almost minimum". $\endgroup$ – Neal Young Aug 23 '18 at 15:15

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