Graph connectivity: Approximation algorithms and applications to protein-protein interaction networks.

详细信息   

• 作者：Gallagher ; Suzanne Renick.
• 学历：Doctor
• 年：2010
• 导师：Gabow, Harold,eadvisorGoldberg, Debra S.,eadvisorBlack, John R.ecommittee memberEhrenfeucht, Andrzejecommittee memberHunter, Lawrenceecommittee memberSkulrattanakulchai, Sanecommittee member
• 毕业院校：University of Colorado
• Department：Computer Science
• ISBN：9781124386799
• CBH：3433292
• Country：USA
• 语种：English
• FileSize：8495762
• Pages：277

文摘

A graph is connected if there is a path between any two of its vertices and k-connected if there are at least k disjoint paths between any two vertices. A graph is k-edge-connected if none of the k paths share any edges and k-vertex-connected or k-connected) if they do not share any intermediate vertices. We examine some problems related to k-connectivity and an application. We have looked at the k-edge-connected spanning subgraph problem: given a k-edge-connected graph, find the smallest subgraph that includes all vertices and is still k-edge-connected. We improved two algorithms for approximating solutions to this problem. The first algorithm transforms the problem into an integer linear program, relaxes it into a real-valued linear program and solves it, then obtains an approximate solution to the original problem by rounding non-integer values. We have improved the approximation ratio by giving a better scheme for rounding the edges and bounding the number of fractional edges. The second algorithm finds a subgraph where every vertex has a minimum degree, then augments the subgraph by adding edges until it is k-edge-connected. We improve this algorithm by bounding the number of edges that could be added in the augmentation step. We have also applied the idea of k-connectivity to protein-protein interaction PPI) networks, biological graphs where vertices represent proteins and edges represent experimentally determined physical interactions. Because few PPI networks are even 1-connected, we have looked for highly connected subgraphs of these graphs. We developed algorithms to find the most highly connected subgraphs of a graph. We applied our algorithms to a large network of yeast protein interactions and found that the most highly connected subgraph was a 16-connected subgraph of membrane proteins that had never before been identified as a module and is of interest to biologists. We also looked at graphs of proteins known to be co-complexed and found that a significant number contained 3-connected subgraphs, one of the features that most differentiated complexes from random graphs.