2014/10/14 by Robert Krauthgamer, Krauthgamer, Robert, Tal Wagner +1
Computer Science · #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Machine Learning and Algorithms #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.1410.3889
openalex publication_date 2014/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the st-cut version the Sparsest-Cut problem, where the goal is to find a cut of minimum sparsity among those separating two distinguished vertices s,t∈ V. Clearly, this problem is at least as hard as the usual (non-st) version. Our main result is a polynomial-time algorithm for the product-demands setting, that produces a cut of sparsity O(√(\OPT)), where \OPT denotes the optimum, and the total edge capacity and the total demand are assumed (by normalization) to be 1. Our result generalizes the recent work of Trevisan [arXiv, 2013] for the non-st version of the same problem (Sparsest-Cut with product demands), which in turn generalizes the bound achieved by the discrete Cheeger inequality, a cornerstone of Spectral Graph Theory that has numerous applications. Indeed, Cheeger's inequality handles graph conductance, the special case of product demands that are proportional to the vertex (capacitated) degrees. Along the way, we obtain an O(log n)-approximation, where n=\cardV, for the general-demands setting of Sparsest st-Cut.