Polymatroidal flows with lower bounds

Multicommodity Flows in Polymatroidal Capacity Networks

A classical result in undirected edge-capaciated networks is the approximate optimality of routing (flow) for multiple-unicast: the min-cut upper bound is within a logarithmic factor of the number of sources of the max flow [2, 3]. In this paper we focus on extending this result to a more general network model, where there are joint polymatroidal constraints on the rates of the edges that meet ...

Flows on Few Paths: Algorithms and Lower Bounds

In classical network flow theory, flow being sent from a source to a destination may be split into a large number of chunks traveling on different paths through the network. This effect is undesired or even forbidden in many applications. Kleinberg introduced the unsplittable flow problem where all flow traveling from a source to a destination must be sent on only one path. This is a generaliza...

Some Lower Bounds for Estrada Index

Lower Bounds

Proof. We induct on d. Exercise 1 proved the base case d = 1. Consider d ≥ 2 and a d-disjunct matrix M with t = t(d,N) rows and N columns. Let N(w) denote the number of columns of M with weight w. (The weight of a column is the number of 1s in it.) A row i ∈ [t] is said to be private for a column j if j is the only column in the matrix having a 1 on row i. If column Mj has weight at most d, the...

Lower Bounds