Towards Maximum Independent Sets on Massive Graphs
Towards Maximum Independent Sets on Massive Graphs Yu Liuy Jiaheng Lu x Hua Yangy Xiaokui Xiaoz Zhewei Weiy yDEKE, MOE and School of Information, Renmin University of China x Department of Computer Science, University of Helsinki, Finland zSchool of Computer Engineering, Nanyang Technological University, Singapore ABSTRACT Maximum independent set (MIS) is a fundamental problem in graph theory and it has important applications in many areas such as so- cial network analysis, graphical information systems and coding theory. The problem is NP-hard, and there has been numerous s- tudies on its approximate solutions. While successful to a certain degree, the existing methods require memory space at least linear in the size of the input graph. This has become a serious concern in !"#$!%&'!(#&)*+,+)*+)-#.+- /"#$!%&'0'#&)*+,+)*+)-#.+- view of the massive volume of today’s fast-growing graphs. Figure 1: An example to illustrate that fv , v g is a maximal inde- In this paper, we study the MIS problem under the semi-external 1 2 pendent set, but fv , v , v , v g is a maximum independent set. setting, which assumes that the main memory can accommodate 2 3 4 5 all vertices of the graph but not all edges. We present a greedy algorithm and a general vertex-swap framework, which swaps ver- duced subgraphs, minimum vertex covers, graph coloring, and tices to incrementally increase the size of independent sets. Our maximum common edge subgraphs, etc. Its significance is not solutions require only few sequential scans of graphs on the disk just limited to graph theory but also in numerous real-world ap- file, thus enabling in-memory computation without costly random plications, such as indexing techniques for shortest path and dis- disk accesses.
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