Min-cuts and Shortest Cycles in Planar Graphs in O(n log log n) Time

TL;DR

This paper introduces a faster deterministic algorithm for finding shortest cycles and minimum cuts in planar graphs, achieving an O(n log log n) runtime by leveraging dense distance graphs and divide-and-conquer techniques.

Contribution

It improves the previous best algorithm for planar graph problems from STOC'11 by a factor of log n using novel dense distance graph methods.

Findings

Achieves O(n log log n) time complexity for shortest cycles and min cuts

Outperforms previous algorithms by a logarithmic factor

Employs dense distance graphs with divide-and-conquer approach

Abstract

We present a deterministic O(n log log n) time algorithm for finding shortest cycles and minimum cuts in planar graphs. The algorithm improves the previously known fastest algorithm by Italiano et al. in STOC'11 by a factor of log n. This speedup is obtained through the use of dense distance graphs combined with a divide-and-conquer approach.