A Graph Theoretical Approach to Network Encoding Complexity

Consider an acyclic directed network G with sources S1, S2, . . . , Sl and distinct sinks R1, R2, . . . , Rl. For i = 1, 2, . . . , l, let ci denote the min-cut between Si and Ri. Then, by Menger’s theorem, there exists a group of ci edge-disjoint paths from Si to Ri, which will be referred to as a group of Menger’s paths from Si to Ri in this paper. Although within the same group they are edge-disjoint, the Menger’s paths from different groups may have to merge with each other. It is known that by choosing Menger’s paths appropriately, the number of mergings among different groups of Menger’s paths is always bounded by a constant, which is independent of the size and the topology of G. The tightest such constant for the all the above-mentioned networks is denoted by M(c1, c2, . . . , c2) when all Si’s are distinct, and by M∗(c1, c2, . . . , c2) when all Si’s are in fact identical. It turns out that M and M∗ are closely related to the network encoding complexity fo...

• Type: Journal
• Year: 2012
• Where: CORR
• Authors: Li Xu, Weiping Shang, Guangyue Han
• Keywords: CORR 2012, Education, Exact Values, Multicast Networks, Theoretical Approach