Loading...

Multi-way sparsest cut problem on trees with a control on the number of parts and outliers

Javadi, R ; Sharif University of Technology | 2021

210 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.dam.2020.11.013
  3. Publisher: Elsevier B.V , 2021
  4. Abstract:
  5. Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for k disjoint subsets of vertices (clusters) whose edge expansions are small and furthermore, the number of vertices that remained in the exterior of the subsets (outliers) is also small. It is proved in Daneshgar et al. (2012) that this problem is NP-hard for trees. Here, we prove that it can be solved in polynomial time for all weighted trees, provided that the search space is restricted to subsets inducing connected subgraphs. The additional constraint has justifications in real-world applications. The proposed algorithm is based on dynamic programming and runs in the worst case in O(k2n3) time, when n is the number of vertices and k is the number of clusters. It also runs in linear time when the number of clusters and the number of outliers are bounded by a constant. © 2020 Elsevier B.V
  6. Keywords:
  7. Dynamic programming ; Expansion ; Forestry ; NP-hard ; Polynomial approximation ; Set theory ; Statistics ; Connected subgraphs ; Disjoint subsets ; Edge expansion ; Normalized cuts ; Number of clusters ; Polynomial-time ; Search spaces ; Weighted tree ; Trees (mathematics)
  8. Source: Discrete Applied Mathematics ; Volume 289 , 2021 , Pages 281-291 ; 0166218X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0166218X20304984