Unified New Techniques for NP-Hard Budgeted Problems with Applications in Team Collaboration, Pattern Recognition, Document Summarization, Community Detection and Imaging

Dorit Hochbaum

2023

Abstract

This paper introduces new techniques for any NP-hard problems formulated as monotone integer programming (IPM) with a budget constraint “budgeted IPM”. Problems of this type have diverse applications, including maximizing team collaboration, the maximum diversity problem, facility dispersion, threat detection, minimizing conductance, clustering, and pattern recognition. We present a unified framework for effective algorithms for budgeted IPM problems based on the Langrangian relaxation of the budget constraint. It is shown that all optimal solutions for all values of the Lagrange multiplier are generated very efficiently, and the piecewise linear concave envelope (convex, for minimization problems) of these solutions has breakpoints that are optimal solutions for the respective budgets. This is used to derive high quality upper and lower bounds for budgets that do not correspond to breakpoints. We show that for all these problems, the weight “perturbation” concept, that was successful for the problem of maximum diversity in enhancing the number and distribution of breakpoints, is applicable. Furthermore, the insights derived from this efficient frontier of solutions, lead to the result that all the respective ratio problems have a solution at the “first” breakpoint, which generalizes the concept of maximum density subgraph.

Paper Citation

in Harvard Style

Hochbaum D. (2023). Unified New Techniques for NP-Hard Budgeted Problems with Applications in Team Collaboration, Pattern Recognition, Document Summarization, Community Detection and Imaging. In Proceedings of the 15th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR; ISBN 978-989-758-671-2, SciTePress, pages 365-372. DOI: 10.5220/0012207200003598

in Bibtex Style

@conference{kdir23,
author={Dorit Hochbaum},
title={Unified New Techniques for NP-Hard Budgeted Problems with Applications in Team Collaboration, Pattern Recognition, Document Summarization, Community Detection and Imaging},
booktitle={Proceedings of the 15th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR},
year={2023},
pages={365-372},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012207200003598},
isbn={978-989-758-671-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR
TI - Unified New Techniques for NP-Hard Budgeted Problems with Applications in Team Collaboration, Pattern Recognition, Document Summarization, Community Detection and Imaging
SN - 978-989-758-671-2
AU - Hochbaum D.
PY - 2023
SP - 365
EP - 372
DO - 10.5220/0012207200003598
PB - SciTePress