Graphs have been widely used due to its expressive power to model complicated relationships. However, given a graph database DG = {g1, g2, · · · , gn}, it is challenging to process graph queries since a basic graph query usually involves costly graph operations such as maximum common subgraph and graph edit distance computation, which are NP-hard. In this paper, we study a novel DSpreserved map...

One of the central parts in the study of combinatorial optimization is to classify the NP-hard optimization problems in terms of their approximability. In this thesis we study the Minimum Vertex Cover (Min-VC) problem and the Minimum Dominating Set (Min-DS) problem in the context of so called power law graphs. This family of graphs is motivated by recent findings on the degree distribution of e...

In this note we consider an example to test three lower bounds presented in Diaconis– Stroock [4] (one by Diaconis and Stroock (DS), another by Sinclair (S) [9], and the third by Jerrum–Sinclair (JS) [8]) of the first positive eigenvalue of a finite graph. The lower bounds are quite sharp in many of the examples studied in [4], and seem to measure the bottlenecks or complexity of the graphs stu...

Graph Proximity Cleansing (GPC) is a string clustering algorithm that automatically detects cluster borders and has been successfully used for string cleansing. For each potential cluster a so-called proximity graph is computed, and the cluster border is detected based on the proximity graph. However, the computation of the proximity graph is expensive and the state-of-the-art GPC algorithms on...