On the sum-max graph partitioning problem

Abstract

Abstract. In this paper we consider the classical combinatorial optimization graph partitioning problem, with Sum-Max as objective function. Given a weighted graph G = (V, E) and a integer k, our objective is to find a k-partition (V1, . . . , V k ) of V that minimizes, where w(u, v) denotes the weight of the edge {u, v} ∈ E. We establish the N P-completeness of the problem and its unweighted version, and the W [1]-hardness for the parameter k. Then, we study the problem for small values of k, and show the membership in P when k = 3, but the N P-hardness for all fixed k ≥ 4 if one vertex per cluster is fixed. Lastly, we present a natural greedy algorithm with an approximation ratio better than k 2 , and show that our analysis is tight.

Bootstrapping Wikipedia to answer ambiguous person name queries

“…The objective then would be to partition the graph into |E | components while minimizing the total weight of the edges between separate components. This problem is known to be NP-hard [35]; hence we follow a relaxed version of this model, where we assign each document to the entity partition for which it exhibits the largest similarity or probability score. To this end, we propose a suite of vector space and probabilistic models, which can be analogously applied to address the above problem.…”