Greedy Approximation Algorithms for Generalized Maximum Flow Problem towards Relation Extraction in Information Networks

Generalized maximum flow problem is a generalization of the traditional maximum flow problem, where each edge e has gain factor γe. When fe units of flow enter edge e=u, v at u, then γe fe units of flow arrive at v. Since relation extraction, which is an important application of the problem, uses large networks such as Wikipedia and DBLP, the computation time to solve the problem is important. However, conventional algorithms for the problem are expensive and do not scale to large graph. Therefore, we propose approximation algorithms based on greedy augmentation and a heuristic initial flow calculation. The experimental result shows that our algorithms are two orders of magnitude faster than a conventional algorithm.

[1]  Pravin M. Vaidya,et al.  Speeding up Karmarkar's algorithm for multicommodity flows , 1996, Math. Program..

[2]  K. Onaga.  Dynamic Programming of Optimum Flows in Lossy Communication Nets , 1966 .

[3]  Danny Dolev,et al.  Theory of Computing and Systems , 1992, Lecture Notes in Computer Science.

[4]  Tomasz Radzik,et al.  Faster algorithms for the generalized network flow problem , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[5]  K. Onaga.  Optimum flows in general communication networks , 1967 .

[6]  Takahiro Hara,et al.  Association thesaurus construction methods based on link co-occurrence analysis for wikipedia , 2008, CIKM '08.

[7]  Andrew V. Goldberg,et al.  Combinatorial algorithms for the generalized circulation problem , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[8]  Christos Faloutsos,et al.  Sampling from large graphs , 2006, KDD '06.

[9]  Lisa Fleischer,et al.  Fast and simple approximation schemes for generalized flow , 2002, Math. Program..

[10]  Andrei Popescu-Belis,et al.  A Random Walk Framework to Compute Textual Semantic Similarity: A Unified Model for Three Benchmark Tasks , 2010, 2010 IEEE Fourth International Conference on Semantic Computing.

[11]  Purnamrita Sarkar,et al.  A Tractable Approach to Finding Closest Truncated-commute-time Neighbors in Large Graphs , 2007, UAI.

[12]  Pravin M. Vaidya,et al.  Speeding-up linear programming using fast matrix multiplication , 1989, 30th Annual Symposium on Foundations of Computer Science.

[13]  Howard D. White,et al.  Author cocitation: A literature measure of intellectual structure , 1981, J. Am. Soc. Inf. Sci..

[14]  Mark A. Fuller,et al.  Faster Algorithms for the Generalized Network Flow Problem , 1998 .

[15]  Éva Tardos,et al.  Simple Generalized Maximum Flow Algorithms , 1998, IPCO.

[16]  James B. Orlin,et al.  Polynomial-Time Highest-Gain Augmenting Path Algorithms for the Generalized Circulation Problem , 1997, Math. Oper. Res..

[17]  Edith Cohen,et al.  New algorithms for generalized network flows , 1994, Math. Program..

[18]  Xinpeng Zhang,et al.  A Generalized Flow-Based Method for Analysis of Implicit Relationships on Wikipedia , 2013, IEEE Transactions on Knowledge and Data Engineering.