Optim Lett DOI 10.1007/s11590-009-0168-z ORIGINAL PAPER Minimum average routing path clustering problem in multi-hop 2-D underwater sensor networks Donghyun Kim · Wei Wang · Ling Ding · Jihwan Lim · Heekuck Oh · Weili Wu Received: 26 May 2009 / Accepted: 9 December 2009 © Springer-Verlag 2009 Abstract In this paper, we introduce a new clustering problem in underwater sensor networks, namely minimum average routing path clustering problem (MARPCP). To deal with the high complexity of MARPCP, we relax it to a special case of mini- mum weight dominating set problem (MWDSP). We show an existing algorithm for MWDSP can produce an approximate solution for MARPCP. Also, we design a con- stant factor approximation algorithm for MARPCP, which is much faster than the first method. Keywords Approximation algorithm · Graph theory · Wireless network clustering · Underwater sensor networks D. Kim (B ) · L. Ding · W. Wu Department of Computer Science, University of Texas at Dallas, Richardson, TX 75083, USA e-mail: donghyunkim@student.utdallas.edu L. Ding e-mail: ling.ding@student.utdallas.edu W. Wu e-mail: weiliwu@utdallas.edu W. Wang Department of Mathematics, Xi’an Jiaotong University, 710049 Xi’an, People’s Republic of China e-mail: wang_weiw@163.com J. Lim · H. Oh Department of Computer Science and Engineering, Hanyang University, Ansan, Gyeonggi 425-791, Republic of Korea e-mail: jhlim@cse.hanyang.ac.kr H. Oh e-mail: hkoh@hanyang.ac.kr 123