a r t i c l e i n f o a b s t r a c t The length-constrained heaviest path (LCHP) in a weighted tree T , where each edge is assigned a weight and a length, is the path P in T with maximum total path weight and total path length bounded by a given value B. This paper presents an O (n log n) time LCHP algorithm which utilizes a data structure constructed from the spine decomposition of the input ...

Given a polyhedral terrain with n vertices, the shortest monotone descent path problem deals with finding the shortest path between a pair of points, called source (s) and destination (t) such that the path is constrained to lie on the surface of the terrain, and 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), whe...

Let s be a source point and t be a destination point inside an n-vertex simple polygon P . Euclidean shortest paths [Lee and Preparata, Networks, 1984; Guibas et al. , Algorithmica, 1987] and minimum-link paths [Suri, CVGIP, 1986; Ghosh, J. Algorithms, 1991] between s and t inside P have been well studied. Both these kinds of paths are simple and piecewise-convex. However, computing optimal pat...

Given two rooted, labeled trees P and T the tree path subsequence problem is to determine which paths in P are subsequences of which paths in T . Here a path begins at the root and ends at a leaf. In this paper we propose this problem as a useful query primitive for XML data, and provide new algorithms improving the previously best known time and space bounds.

In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P , the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linearspace algorithm with O(n log n) running time for n-vertex planar directed graphs. The previous best time boun...

1.1. Gaussian random fields on manifolds. Let X(p), p ∈ M̃ , be a realvalued random field on an orientable manifold M̃ . In this article, we consider a Gaussian random field with a smooth sample path and one-dimensional standard normal marginals (i.e., X(p) ∼ N(0, 1) for each p ∈ M̃). Let r(p, q) = Cov(X(p), X(q)) denote the covariance function. If r(p, q) is sufficiently smooth in a neighborhood ...

Let λ ∈ P . The straight line path to λ is the map pλ : [0, 1]→ hR given by pλ(t) = λt. Let `1, `2 ∈ R≥0. The concatenation of maps p1 : [0, `1] → hR and p2 : [0, 1] → hR is the map p1 ⊗ p2 : [0, `1 + `2]→ hR given by (p1 ⊗ p2)(t) = { p1(t), for t ∈ [0, `1], p1(`1) + p2(t− `1), for t ∈ [`1, `1 + `2]. Let r, ` ∈ R≥0. The r-stretch of a map p : [0, `]→ hR is the map rp : [0, `]→ hR given by (rp)(...

MDVSP k k p p k k p K k p k p k ip K k p k p k p k k k ip k k p k j ij i i ij i i p K k x K k n x N i x a x c K k n N i p a p c K k K N j i t d s t A j i A K N j i j i d N i s N i t N K k k k min depot at vehicles of number available : otherwise 0 ; task covers path if 1 path of cost : depot to and from paths of set : , for , if) , (arcs; of set : , for , node to node from go to time : for task...

Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum mechanics. 1. It is well known that dynamical evolution of any one-dimensional quantum-mechanical system, described by a wave function Ψ(x, t), is given by Ψ(x ′′ , t...