Let G = (V,E) be a graph with vertex set V and edge set E and let T be a subset of V . A terminal path cover PC of G with respect to T is a set of pairwise vertex-disjoint paths of G, such that all vertices of G are visited by exactly one path of PC and all vertices in T are end vertices of paths in PC. The terminal path cover problem is to find a terminal path cover of G of minimum cardinality...

1, Path calibration using the aftershock The calibration is obtained by convolving the mainshock data with the 1D synthetic of the aftershock and then deconvolving with the data of the aftershock. We have applied a 1Hz low-pass filter to the calibrated data because the effect of 3D slab structure in the source region cannot be ignored at higher frequency (>1Hz) (Fig.S1). The mechanism of the af...

We give a partial description of the (s, t)− p-path polytope of a directed graph D which is the convex hull of the incidence vectors of simple directed (s, t)-paths in D of length p. First, we point out how the (s, t) − p-path polytope is located in the family of path and cycle polyhedra. Next, we give some classes of valid inequalities which are very similar to inequalities which are valid for...

Let T be a rooted tree. A path reversal at a node x in T is performed by traversing the path from x to the tree root r and making x the parent of each node on the path other than X. Thus x becomes the new tree root. (See Fig. 1). The cost of the reversal is the number of edges on the path reversed. Path reversal is a variant of the standard path compression algorithm for maintaining disjoint se...

Abstract. An analytic singular value decomposition (ASVD) of a path of matrices E(t) is an analytic path of factorizations E(t) = X(t)S(t)Y (t) where X(t) and Y (t) are orthogonal and S(t) is diagonal. The diagonal entries of S(t) are allowed to be either positive or negative and to appear in any order. For an analytic path matrix E(t) an ASVD exists, but this ASVD is not unique. We present two...

Given a weighted graph G = (V ,E) with a source s and a destination t , a traveler has to go from s to t . However, some of the edges may be blocked at certain times, and the traveler only observes that upon reaching an adjacent site of the blocked edge. Let P = {PG(s, t)} be the set of all paths from s to t . The risk of a path is defined as the longest travel under the assumption that any edg...

A set P of edge-disjoint paths in a graph G is called an edge-covering of G if every edge of G is contained in a path of P. The path edge-covering number of G is then defined as the smallest number p(G) of paths in such an edge-covering of G. This parameter appeared in the study of certain models of information retrieval structures (see, e. g., [6]). If we are considering a tree T , then it is ...

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...

In this paper, we study a variant of the path cover problem, namely, the terminal path cover problem. Given a graph G and a subset T of vertices of G, a terminal path cover of G with respect to T is a set of pairwise vertex-disjoint paths PC that covers the vertices of G such that the vertices of T are all endpoints of the paths in PC. The terminal path cover problem is to find a terminal path ...