We present an exact algorithm for computing an earliest arrival flow in a discrete time setting on series-parallel graphs. In contrast to previous results for the earliest arrival flow problem this algorithm runs in polynomial time.

In recent empirical studies we have shown that many interesting cost-based abduction problems can be solved efficiently by considering the linear program relaxation of their integer program formulation. We tie this to the concept of total unimodularity from network flow analysis, a fundamental result in polynomial solvability. From this, we can determine the polynomial solvability of abduction ...

design of crystal-like lattices can be achieved by using some net operations. hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. the networks herein presented are related to the dyck graph and described in terms of omega polynomial and piv polynomials.

When a flow is not allowed to be reoriented the Maximum Residual Flow Problem with k-Arc Destruction is known to be NP -hard for k = 2. We show that when a flow is allowed to be adaptive the problem becomes polynomial for every fixed k.

We analyze the asymptotic behavior of the Flow Deviation Method, first presented in 1971 by Fratta, Gerla and Kleinrock, and show that when applied to packing linear programs such as the maximum concurrent flow problem, it yields a fully polynomial-time approximation scheme.