We present a data mining approach for reducing the search space of local search algorithms in large-scale set partitioning problems (SPPs). We construct a k-nearest neighbor graph by extracting variable associations from the instance to be solved, in order to identify promising pairs of flipping variables in the large neighborhood search. We incorporate the search space reduction technique into...

The commuting graph of a finite non-abelian group G with center Z(G), denoted by ?c(G), is simple undirected whose vertex set G?Z(G), and two distinct vertices x y are adjacent if only xy=yx. Alwardi et al. (Bulletin, 2011, 36, 49-59) defined the common neighborhood matrix CN(G) energy Ecn(G) G. A called CN-hyperenergetic Ecn(G)>Ecn(Kn), where n=|V(G)| Kn denotes complete on n vertices. Two ...

In this paper we study proximity structures like Delaunay triangulations based on geometric graphs, i.e. graphs which are subgraphs of the complete geometric graph. Given an arbitrary geometric graph G, we define several Voronoi diagrams, Delaunay triangulations, relative neighborhood graphs, Gabriel graphs and then study their complexities when G is a general geometric graph or G is some speci...

In this paper, we investigate sufficient conditions on the neighborhood of independent vertices which imply that a graph contains k independent cycles or chorded cycles. This is related to several results of Corrádi and Hajnal, Justesen, Wang, and Faudree and Gould on graphs containing k independent cycles, and Finkel on graphs containing k chorded cycles. In particular, we establish that if in...

We present a new graph based semi-supervised learning algorithm, using multiway cut on a neighborhood graph to achieve an optimum classification. We also present a graph based feature selection algorithm utilizing the global structure of the graph derived from both labeled and unlabeled examples. With respect to the experiments we conducted, both of our approaches are proved to have a promising...

Previously, we proposed a physically inspired rule to organize the data points in a sparse yet effective structure, called the in-tree (IT) graph, which is able to capture a wide class of underlying cluster structures in the datasets, especially for the density-based datasets. Although there are some redundant edges or lines between clusters requiring to be removed by computer, this IT graph ha...

We consider the complexity of the emptiness problem for various classes of graph languages deened by eNCE (edge label neighborhood controlled embedding) graph grammars. In particular, we show that the emptiness problem is undecidable for general eNCE graph grammars, DEXPTIME-complete for connuent and boundary eNCE graph grammars, PSPACE-complete for linear eNCE graph grammars, NL-complete for d...

eNCE (edge label neighborhood controlled) graph grammars belong to the most powerful graph rewriting systems with single-node graphs on the left-hand side of the productions. From an algorithmic point of view, connuent and boundary eNCE graph grammars are the most interesting subclasses of eNCE graph grammars. In connuent eNCE graph grammars, the order in which nonterminal nodes are substituted...