The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter. Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted $m$-edge and $n$-node gr…
We have improved the additive distortion bounds for spanners and emulators for many values of ϵ below the n4/3 edge threshold. The main open question of spanner research still remains: do there exist spanners or emulators on O(n4/3−δ) edges with add…
Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of applications. Sim…
Here we apply our framework to more contexts. The proofs of some our results in this section will be restricted to sketches, and full proofs of Theorems 3 and 4 can be found in the appendix.
We consider several well-studied problems in dynamic algorithms and prove that sufficient progress on any of them would imply a breakthrough on one of five major open problems in the theory of algorithms: 1. Is the 3SUM problem on $n$ numbers in $…
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