Multiway k-Cut in Static and Dynamic Graphs: A Maximum Entropy Principle Approach

Mayank Baranwal, Amber Srivastava, Srinivasa M. Salapaka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This work presents a maximum entropy principle based algorithm for solving minimum multiway k-cut problem defined over static and dynamic digraphs. A multiway k-cut problem requires partitioning the set of nodes in a graph into k subsets, such that each subset contains one prespecified node, and the corresponding total cut weight is minimized. These problems arise in many applications and are computationally complex (NP-hard). In the static setting this article presents an approach that uses a relaxed multiway k-cut cost function; we show that the resulting algorithm converges to a local minimum. This iterative algorithm is designed to avoid poor local minima with its run-time complexity as ~ O(kIN3), where N is the number of vertices and I is the number of iterations. In the dynamic setting, the edge-weight matrix has an associated dynamics with some of the edges in the graph capable of being influenced by an external input. The objective is to design the dynamics of the controllable edges so that multiway k-cut value remains small (or decreases) as the graph evolves under the dynamics. Also it is required to determine the time-varying partition that defines the minimum multiway k-cut value. Our approach is to choose a relaxation of multiway k-cut value, derived using maximum entropy principle, and treat it as a control Lyapunov function to design control laws that affect the weight dynamics. Simulations on practical examples of interactive foreground-background segmentation, minimum multiway k-cut optimization for non-planar graphs and dynamically evolving graphs that demonstrate the efficacy of the algorithm, are presented.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3948-3953
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Externally publishedYes
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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