On size-constrained minimum s–t cut problems and size-constrained dense subgraph problems
In some application cases, the solutions of combinatorial optimization problems on graphs should satisfy an additional vertex size constraint. In this paper, we consider size-constrained minimum s–t cut problems and size-constrained dense subgraph problems. We introduce the minimum s–t cut with at-least-k vertices problem, the minimum s–t cut with at-most-k vertices problem, and the minimum s–t cut with exactly k vertices problem. We prove that they are NP-complete. Thus, they are not polynomially solvable unless P = NP. On the other hand, we also study the densest at-least-k-subgraph problem (DalkS) and the densest at-most-k-subgraph problem (DamkS) introduced by Andersen and Chellapilla [1]. We present a polynomial time algorithm for DalkS when k is bounded by some constant c. We also present two approximation algorithms for DamkS. In conclusion, the first approximation algorithm for DamkS has an approximation ratio of n-1/k-1, where n is the number of vertices in the input graph. The second approximation algorithm for DamkS has an approximation ratio of O (nδ), for some δ < 1/3.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- DEAC05-00OR22725; AC05-00OR22725
- OSTI ID:
- 1581189
- Alternate ID(s):
- OSTI ID: 1331085; OSTI ID: 1359929
- Journal Information:
- Theoretical Computer Science, Journal Name: Theoretical Computer Science Vol. 609 Journal Issue: P2; ISSN 0304-3975
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- Netherlands
- Language:
- English
Web of Science
Cache Aided Decode-and-Forward Relaying Networks: From the Spatial View
|
journal | January 2018 |
Similar Records
Finding minimum-quotient cuts in planar graphs
Finding minimum-quotient cuts in planar graphs