Abstract. Let G = (N,A) be an undirected graph with n nodes and m arcs, a designated source node s and a sink node t. This paper addresses sensitivity analysis questions concerning the shortest s-t path (SP) problem in G and the maximum capacity s-t path (MCP) problem in G. Suppose that P* is a shortest s-t path in G with respect to a nonnegative distance vector c. For each arc e ∈ A, the lower...

Our rigorous path integral is extended to quantum evolution on metricaffine manifolds. 1 Path Integrals on Euclidean Spaces. Consider the evolution operator U [ψ(t, q)] = ψ(t, q), t ≥ t, of the quantum evolution equation on L(R): h̄ i ∂ψ(t, q)/∂t+ f(t, q, h̄ i ∂/∂q)ψ(t, q) = 0. Here the operator f(t, q, h̄ i ∂/∂q) is the standard quantization of a classical timedependent quasi-Hamiltonian f(t, q, ...

Given a convex polytope P with n edges in R3, we present a relatively simple algorithm that preprocesses P in O(n) time, such that, given any two points s, t ∈ ∂P , and a parameter 0 < ε ≤ 1, it computes, in O((log n)/ε1.5 + 1/ε3) time, a distance 1P(s, t), such that dP(s, t) ≤ 1P(s, t) ≤ (1+ ε)dP(s, t), where dP(s, t) is the length of the shortest path between s and t on ∂P . The algorithm als...

We consider an undirected graph G = (VG,EG) with a set T ⊆ VG of terminals, and with nonnegative integer capacities c(v) and costs a(v) of nodes v ∈ VG. A path in G is a T -path if its ends are distinct terminals. By a multiflow we mean a function F assigning to each T -path P a nonnegative rational weight F(P ), and a multiflow is called feasible if the sum of weights of T -paths through each ...

The natural linear programming formulation of the maximum s-t-flow problem in path variables has a dual linear program whose underlying polyhedron is the dominant P↑ s-t-cut of the s-t-cut polytope. We present a complete characterization of P↑ s-t-cut with respect to vertices, facets, and adjacency.

Consider a tree T with a number of extra edges (the bridges) added. We consider the notion of diameter, that is obtained by admitting only paths p with the property that for every bridge b in path p, no edge that is on the unique path (in T) between the endpoints of b is also in p or on the unique path between the two endpoints of any other bridge in p. (Such a path is called non-reversing.) We...

The natural linear programming formulation of the maximum s-t-flow problem in path variables has a dual linear program whose underlying polyhedron is the dominant P↑ s-t-cut of the s-t-cut polytope. We present a complete characterization of P↑ s-t-cut with respect to vertices, facets, and adjacency.