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...

A path from a point s to a point t on the surface of a polyhedral terrain is said to be descent if for every pair of points p = (x(p), y(p), z(p)) and q = (x(q), y(q), z(q)) on the path, if dist(s, p) < dist(s, q) then z(p) ≥ z(q), where dist(s, p) denotes the distance of p from s along the aforesaid path. Although an efficient algorithm to decide if there is a descending path between two point...

We show that, for a stationary version of Hammersley’s process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly North–East path L(t, t) from (0,0) to (t, t) is equal to 2E(t −X(t))+, where X(t) is the location of a second class particle at time t . This implies that both E(t −X(t))+ and the variance of L(t, t) ...

Let T be a tournament and let D be a digraph. We say that T contains D if D is a subgraph of T. The order of a digraph D, denoted by |D|, is its number of vertices. Let x and y be two vertices of T. We write x y if (x, y) is an arc of T. Likewise, let X and Y be two subdigraphs of T. We write X Y if x y for all pairs (x, y) # V(X )_V(Y ). Let A1 , A2 , ..., Ak be a family of subdigraphs of T. W...

In this short article, we observe that the path of particle of mass $m$ moving along $mathbf{r}= mathbf{r}(t)$ under pseudo-force $mathbf{A}(t)$, $t$ denotes the time, is given by $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{A}(t)) dt +mathbf{c}$. We also observe that the effective force $mathbf{F}_e$ on that particle due to pseudo-force $mathbf{A}(t)$, is given by $ mathbf{F}_e= mathbf{F} mat...

Let (X(t)) be a risk process with reserve-dependent premium rate, delayed claims and initial capital u. Consider a class of risk processes {(Xε(t)) : ε > 0} derived from (X(t)) via scaling in a slow Markov walk sense, and let Ψε(u) be the corresponding ruin probability. In this paper we prove sample path large deviations for (X(t)) as ε → 0. As a consequence, we give exact asymptotics for log Ψ...

Best-rst search algorithms have been widely used to nd a minimum cost path in graph search. To formulate certain problems involving temporal events, it is at times instrumental to use graphs whose edge costs are time-dependent. In such a graph, shortest paths are dependent on time at which traversal in the graph begins. Typically, structural changes in t occur at discrete points in t, where t i...

Let v be a bounded function with bounded support in Rd, d ≥ 3. Let x, y ∈ Rd. Let Z(t) denote the path integral of v along the path of a Brownian bridge in Rd which runs for time t, starting at x and ending at y. As t → ∞, it is perhaps evident that the distribution of Z(t) converges weakly to that of the sum of the integrals of v along the paths of two independent Brownian motions, starting at...

W e extend the path status graph (PSG) method of delay faul t simulation to sequential circuits. By devising a layered PSG and restricting the number of timeframes over which a fault mus t be detected, we preserve the non-enumerative nature of the simulation algorithm. T h e program is capable of simulating a wide variety of circuits (synchronous, asynchronous, multiple-clock and tri-state logi...

In this paper we prove a large deviation principle for the empirical drift of a onedimensional Brownian motion with self-repellence called the Edwards model. Our results extend earlier work in which a law of large numbers, respectively, a central limit theorem were derived. In the Edwards model a path of length T receives a penalty eT , where HT is the self-intersection local time of the path a...