On the Langberg–Médard multiple unicast conjecture

Kai Cai () and Guangyue Han ()
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Kai Cai: The University of Hong Kong
Guangyue Han: The University of Hong Kong

Journal of Combinatorial Optimization, 2017, vol. 34, issue 4, No 8, 1114-1132

Abstract: Abstract A version of the multiple unicast conjecture, proposed by Langberg and Médard (in: Proceedings of 47th annual Allerton, 2009), says that, there exists an undirected fractional multi-commodity flow, or simply, multi-flow, with rate $$(1,1,\ldots ,1)$$ ( 1 , 1 , … , 1 ) for strongly reachable networks. In this paper, we propose a nonsmooth matrix optimization problem to attack this conjecture: By giving upper and lower bounds on the objective value, we prove that there exists a multi-flow with rate at least $$(\frac{8}{9}, \frac{8}{9}, \ldots , \frac{8}{9})$$ ( 8 9 , 8 9 , … , 8 9 ) for such networks; on the other hand though, we show that the rate of any multi-flow constructed using this framework cannot exceed $$(1,1,\ldots ,1)$$ ( 1 , 1 , … , 1 ) .

Keywords: Multiple commodity flow; Nonsmooth optimization; Multiple unicast conjecture (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-017-0132-2

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