A colouring of a strongly regular graph is an allocation of colours (or treatments) to the vertices of the graph. Such a colouring is balanced if every pair of distinct colours occurs equally often on the ends of an edge. When the graph is the complete regular multipartite graph a balanced colouring is just a balanced incomplete-block design, or 2-design. Some constructions are given. For examp...

We introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem: Let G=(V,E) be a connected graph with a weight (supply/demand) function p:V→ {−1,+1} satisfying p(V )= ∑ j∈V p(j)=0. The objective is to partition G into (V1, V2) such that G[V1] and G[V2] are connected, |p(V1)|, |p(V2)|≤cp, and max{ |V1| |V2| , |V2| |V1|}≤cs, for some constants cp and cs. When G is 2-connec...

Similarity analytic techniques such as distance based joins and regularized learningmodels are critical tools employed in numerous data mining and machine learning tasks. We focus on two typical techniques in the context of large scale data and distributed clusters. Advanced distance metrics such as the Earth Mover’s Distance (EMD) are usually employed to capture the similarity between data dim...

Accurate and fast path computation is essential for applications such as onboard navigation systems and traffic network routing. While a number of heuristic algorithms have been developed in the past few years for faster path queries, the accuracy of them are always far below satisfying. In this paper, we first develop an agglomerative graph partitioning method for generating high balanced trav...

the wiener index w(g) of a connected graph g is defined as the sum of the distances betweenall unordered pairs of vertices of g. the eccentricity of a vertex v in g is the distance to avertex farthest from v. in this paper we obtain the wiener index of a graph in terms ofeccentricities. further we extend these results to the self-centered graphs.

We introduce and study online balanced coloring games on the random graph process. The game is played by a player we call Painter. Edges of the complete graph with n vertices are introduced two at the time, in a random order. For each pair of edges, Painter immediately and irrevocably chooses one of the two possibilities to color one of them red and the other one blue. His goal is to avoid crea...