Preliminaries. A graph database G is a finite, directed, edge-labeled, multigraph defined by G = 〈N,Σ,E〉, where N is a finite set of nodes (vertices), Σ is a set of labels, E is a set of directed, labeled edges, and E ⊆ N ×Σ×N . A path p in G is defined as a sequence of n0a0n1 · · · nk−1ak−1nk where ni ∈ N , ai ∈ Σ, and 〈ni, ai, ni+1〉 ∈ E for 0 ≤ i ≤ k. We call the sequence of edge labels Σ∗ of...

Abstract Elastic thermobarometry of host-inclusion systems for back-calculating pressure (P) and temperature (T) conditions inclusion entrapment relies on the assumption that hostinclusion rheology is purely elastic. In this study, we have explored both elastic non-elastic behavior zircon-in-garnet (ZiG) by in situ Raman spectroscopy at high T ambient P. We show upon heating, plastic relaxation...

We consider searching problems in robotics that a robot has to nd a path to a target by traveling in an unknown star-shaped polygon P. The goal is to minimize the ratio of the distance traveled by the robot to the length of the shortest start-to-target path. Let s be a starting point in P. We rst present a competitive strategy to nd a path from s to the closest kernel point k of P. The length o...

Let N = (V, E, c, /) be a network, where G = (V, E), (VI = n and (El = m, is a directed graph, c(e) > 0 is the capacity and I(e) 2 0 is the lead time for each edge e E E. The transmission time to send u units of data from a given source s to a destination t using path p is T(a,p) = I(p) + &, where 1(p) is the sum of the lead times of the edges in p, and c(p) is the minimum capacity of the edges...

Given a simple polygon P without holes all of whose edges are axis-parallel, a rectilinear path in P is a path that consists of axis-parallel segments only and does not cross any edge of P. The length of such a path is defined as the number of segments it consists of and the rectilinear link distance between two points in P is defined as the length of the shortest path connecting the two points...

Let C m T denote the Kronecker product of a cycle C m and a tree T. If m is odd, then C m T is connected, otherwise this graph consists of two isomorphic components. This paper presents a scheme which constructs a long cycle in each component of C m T, where T satisses certain degree constraints. The cycle thus traced is shown to be a dominating set, and in some cases, a vertex cover of that co...

Graphs and digraphs treated here are finite and simple. Let G = (V (G), E(G)) be a connected graph with vertex set V (G) and edge set E(G), and D the symmetric digraph corresponding toG. SetD(G) = {(u, v), (v, u) | uv ∈ E(G)}. For e = (u, v) ∈ D(G), set u = o(e) and v = t(e). Furthermore, let e−1 = (v, u) be the inverse of e = (u, v). A path P of length n in G is a sequence P = (e1, · · · , en)...

Let P be a path between two points s and t in a polygonal subdivision T with obstacles and weighted regions. Given a relative error tolerance ε ∈ (0, 1), we present the first algorithm to compute a path between s and t that can be deformed to P without passing over any obstacle and the path cost is within a factor 1+ ε of the optimum. The running time is O( 3 ε2 knpolylog(k, n, 1 ε )), where k ...