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Open AccessArticle

New Bipartite Graph Techniques for Irregular Data Redistribution Scheduling

by Qinghai Li 1 and Chang Wu Yu 2,*
1
Department of Electronic Engineering, Zhejiang Industry and Trade Vocational College, East Road 717, Wenzhou 325003, China
2
Department of Computer Science and Information Engineering, Chung Hua University, No.707, Sec.2, WuFu Road, Hsinchu 30012, Taiwan
*
Author to whom correspondence should be addressed.
Algorithms 2019, 12(7), 142; https://doi.org/10.3390/a12070142
Received: 26 May 2019 / Revised: 10 July 2019 / Accepted: 14 July 2019 / Published: 16 July 2019
For many parallel and distributed systems, automatic data redistribution improves its locality and increases system performance for various computer problems and applications. In general, an array can be distributed to multiple processing systems by using regular or irregular distributions. Some data distribution adopts BLOCK, CYCLIC, or BLOCK-CYCLIC to specify data array decomposition and distribution. On the other hand, irregular distributions specify a different-size data array distribution according to user-defined commands or procedures. In this work, we propose three bipartite graph problems, including the “maximum edge coloring problem”, the “maximum degree edge coloring problem”, and the “cost-sharing maximum edge coloring problem” to formulate these kinds of distribution problems. Next, we propose an approximation algorithm with a ratio bound of two for the maximum edge coloring problem when the input graph is biplanar. Moreover, we also prove that the “cost-sharing maximum edge coloring problem” is an NP-complete problem even when the input graph is biplanar. View Full-Text
Keywords: data redistribution; scheduling; edge coloring; approximation algorithms; graph techniques; bipartite graphs; algorithm design data redistribution; scheduling; edge coloring; approximation algorithms; graph techniques; bipartite graphs; algorithm design
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Li, Q.; Yu, C.W. New Bipartite Graph Techniques for Irregular Data Redistribution Scheduling. Algorithms 2019, 12, 142.

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