Core Concepts
The author proposes the kDC-two algorithm to enhance time complexity and practical performance in computing maximum defective cliques.
Abstract
The content discusses the challenges of improving time complexities for maximum defective clique computation. It introduces the kDC-two algorithm, utilizing a two-stage approach and the diameter-two property for efficiency. The algorithm aims to find the largest defective clique while addressing real-world graph complexities.
Key points include:
- Introduction to defective cliques as a relaxation of traditional cliques.
- Explanation of existing algorithms like kDC and their limitations.
- Proposal of the kDC-two algorithm with improved time complexity.
- Utilization of degeneracy ordering and reduction rules for efficient computation.
- Detailed analysis of the branching process and search tree traversal.
- Application of the diameter-two property for pruning in large defective cliques.
The study concludes with empirical evaluations showing significant improvements over existing algorithms.
Stats
kDC runs in O∗(훾푛 푘 ) time, where 훾푘 is a constant smaller than two.
kDC-two improves base and exponent of exponential time complexity.
Extensive empirical studies on 290 graphs show superior performance of kDC-two.