Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
A cluster-based approach for routing in dynamic networks
ACM SIGCOMM Computer Communication Review
Efficient identification of Web communities
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
New methods to color the vertices of a graph
Communications of the ACM
IEEE Intelligent Systems
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Variable neighborhood search for the maximum clique
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
Optimal Protein Structure Alignment Using Maximum Cliques
Operations Research
A Convex Quadratic Characterization of the Lovász Theta Number
SIAM Journal on Discrete Mathematics
An Efficient Branch-and-bound Algorithm for Finding a Maximum Clique with Computational Experiments
Journal of Global Optimization
Simple ingredients leading to very efficient heuristics for the maximum clique problem
Journal of Heuristics
Isolation concepts for efficiently enumerating dense subgraphs
Theoretical Computer Science
Enumeration of isolated cliques and pseudo-cliques
ACM Transactions on Algorithms (TALG)
Extended and discretized formulations for the maximum clique problem
Computers and Operations Research
Hiding in plain sight: criminal network analysis
Computational & Mathematical Organization Theory
A sequential elimination algorithm for computing bounds on the clique number of a graph
Discrete Optimization
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Given a graph G=(V,E) and a clique C of G, the edge neighborhood of C can be defined as the total number of edges running between C and V@?C, being denoted by N(C). The density of the edge neighborhood N(C) can be set as the ratio (|N(C)|/(|C|.|V@?C|)). This paper addresses maximum/minimum edge neighborhood and neighborhood density cliques in G. Two versions will be undertaken, by fixing, or not, the size of the cliques. From an optimization point of view these problems do not bring much novelty, as they can be seen as particular or special versions of weighted clique problems. However, from a practical point of view, they concentrate on certain kinds of properties of cliques, rather than their size, revealing clique's engagement in the graph. In fact, a maximum edge neighborhood clique should be strongly embraced in the graph, while a minimum edge neighborhood clique should reveal an almost isolated strong component. In particular, special versions of the new problems allow to distinguish among cliques of the same size, namely among possible tied maximum cliques in the graph. We propose node based formulations for these edge based clique related problems. Using these models, we present computational results and suggest applications where the new problems can bring additional insights.