Lecture 8: Undirected Connectivity is in logspace
نویسنده
چکیده
Clearly, any of the standard search algorithms (depth-first-search, breadth-first-search etc.) solve USTCONN in linear time. Thus, the time complexity of USTCONN is wellunderstood. What we would be interested in today’s lecture is the same complexity of USTCONN. It is to be noted that the standard search algorithms perform poorly with respect to space (this is because their implementation requires a stack or queue which in the worst case could be as large as the graph). The question we will concern ourselves is the following: Is USTCONN in Logspace. In other words, does there exist a deterministic logspace algorithm that can decide connectivity in an undirected graph. Reingold resolved this question positively and gave a logspace algorithm for USTCONN using the zig-zag product. Before that, we will briefly look at the history of USTCONN.
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