Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the variables involved that is manifestly inconsistent. On the other hand, a phase space path integral based on coherent states entails variables that exhibit a self...

The Shortest Path Problem with Resource Constraints is a common subproblem in many Branch-Cut-and-Price algorithms (BCP), e.g., routing and scheduling problems. This paper presents a general label-setting algorithm for solving various shortest path problems. An integration of the ‘Shortest Path Problem with Resource Constraints and k-cycle elimination’ with the ‘Partial Elementarity’ is introdu...

In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest s-t path P such that no path in X is a subpath of P . Path P is allowed to repeat vertices and edges. We call each path in X an exception, and our desired path a shortest exception avoiding path. We formulate a new ver...

Let T be a tree that is embedded in the plane and let ∆ > 0 be a real number. The aim is to preprocess T into a data structure, such that, for any query polygonal path Q, we can decide if T contains a path P whose Fréchet distance δF (P,Q) to Q is less than ∆. For any real number ε > 0, we present an efficient data structure that solves an approximate version of this problem, for the case when ...

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...

A binary matrix satisfies the consecutive ones property (C1P) if its columns can be permuted such that the 1s in each row of the resulting matrix are consecutive. Equivalently, a family of sets F = {Q1, . . . , Qm}, where Qi ⊆ R for some universe R, satisfies the C1P if the symbols in R can be permuted such that the elements of each set Qi ∈ F occur consecutively, as a contiguous segment of the...

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...

If x is a vertex of a tree T of radius r, if k and 1 are integers, if 0 < k < r, 0 < I < r, and if P is an L-path with one end at x, then define /3(x; k,P) to be the number of vertices of T that are reachable from x via the l-path P and that are outside of the k-ball about x. That is, fl(x; k, P) = 1 (y E V( T ): y is reachable from x via P, d(x, y) > k} I. Define the k-ball l-path branch weigh...

The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in R3, two points s, t ∈ P , and a parameter ε > 0, it computes a path between s and t on P whose lengt...