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Problems known to be open in the literature and any problem that, after being posed, is decided to be open by the community.
31
votes
Open problems on the frontiers of TCS
Here are three in shortest paths research:
$1$. Is there a linear time algorithm for single source shortest paths in directed graphs with nonnegative weights, at least in the word-RAM model of comput …
28
votes
Accepted
Optimal algorithm for finding the girth of a sparse graph?
Here's what I know about the girth problem in undirected unweighted graphs.
First of all, if the girth is even, you can determine it in $O(n^2)$ time- this is an old result of Itai and Rodeh (A. Itai …