We derive the performance of the exponential symmetric longest queue system from two variants: a longest queue system with Threshold Rejection of jobs and one with Threshold Addition of jobs. Van Houtum, Geert-Jan Adan, Ivo van der Wal, Jan If G is 2-connected and cubic, then every longest cycle in G has a chord. If G is 2-connected and cubic, then every longest cycle in G has a chord.If a graph G is 3-connected and has minimum degree at least 4, then some longest cycle in G has a chord. If a graph G is 3-connected and has minimum degree at least 4, then some longest cycle in G has a chord. For the extensively studied longest common subsequence problem, comparable speedups have not been achieved for small. Finally, we introduce the problem of longest common weakly-increasing (or non-decreasing) subsequences (LCWIS), for which we present an -time algorithm for the 3-letter alphabet case. For two sequences of lengths n and m, where m⩾n, we present an algorithm with an output-dependent expected running time of and O(m) space, where â„“ is the length of an LCIS, σ is the size. In both cases, our algorithms are conceptually quite simple but rely on existing sophisticated data structures.We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For kâ©❣ length-n sequences we present an algorithm which improves the previous best bound by more than a factor k for many inputs. Of the alphabet, and Sort is the time to sort each input sequence. Kutz, Martin Brodal, Gerth Stølting Kaligosi, Kanela Faster Algorithms for Computing Longest Common Increasing Subsequences
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