Min-Max Graph Partitioning and Small Set Expansion

Streaming Min-max Hypergraph Partitioning

In many applications, the data is of rich structure that can be represented by a hypergraph, where the data items are represented by vertices and the associations among items are represented by hyperedges. Equivalently, we are given an input bipartite graph with two types of vertices: items, and associations (which we refer to as topics). We consider the problem of partitioning the set of items...

Sum-Max Graph Partitioning Problem

This paper tackles the following problem: given a connected graph G = (V,E) with a weight function on its edges and an integer k ≤ |V |, find a partition of V into k clusters such that the sum (over all pairs of clusters) of the heaviest edges between the clusters is minimized. We first prove that this problem (and even the unweighted variant) cannot be approximated within a factor of O(n1− ) u...

A Min-max Cut Algorithm for Graph Partitioning and Data Clustering

High Quality Hypergraph Partitioning via Max-Flow-Min-Cut Computations

In this thesis, we introduce a framework based on Max-Flow-Min-Cut computations for improving balanced k-way partitions of hypergraphs. Currently, variations of the FM heuristic [17] are used as local search algorithms in all state-of-the-art multilevel hypergraph partitioners. Such move-based heuristics have the disadvantage that they only incorporate local information about the problem struct...

Graph Searching and a Min-Max Theorem for Tree-Width

The tree-width of a graph G is the minimum k such that G may be decomposed into a “treestructure” of pieces each with at most k + 1 vertices. We prove that this equals the maximum k such that there is a collection of connected subgraphs, pairwise intersecting or adjacent, such that no set of ≤ k vertices meets all of them. A corollary is an analogue of LaPaugh’s “monotone search” theorem for co...