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Title: A Simple Framework for Finding Balanced Sparse Cuts via APSP
We present a very simple and intuitive algorithm to find balanced sparse cuts in a graph via shortest-paths. Our algorithm combines a new multiplicative-weights framework for solving unit-weight multi-commodity flows with standard ball growing arguments. Using Dijkstra's algorithm for computing the shortest paths afresh every time gives a very simple algorithm that runs in time Õ(m^2/ø) and finds an Õ(ø)-sparse balanced cut, when the given graph has a ø-sparse balanced cut. Combining our algorithm with known deterministic data-structures for answering approximate All Pairs Shortest Paths (APSP) queries under increasing edge weights (decremental setting), we obtain a simple deterministic algorithm that finds m^{o(1)}ø-sparse balanced cuts in m^{1+o(1)}/ø time. Our deterministic almost-linear time algorithm matches the state-of-the-art in randomized and deterministic settings up to subpolynomial factors, while being significantly simpler to understand and analyze, especially compared to the only almost-linear time deterministic algorithm, a recent breakthrough by Chuzhoy-Gao-Li-Nanongkai- Peng-Saranurak (FOCS 2020).  more » « less
Award ID(s):
Author(s) / Creator(s):
Telikepalli Kavitha and Kurt Mehlhorn
Date Published:
Journal Name:
2023 Symposium on Simplicity in Algorithms, SOSA 2023, Florence, Italy
Page Range / eLocation ID:
42 - 55
Medium: X
Sponsoring Org:
National Science Foundation
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