The article presents an approach to the maximum flow problem in parametric networks with linear capacity functions of a single parameter, based on the concept of shortest conditional augmenting directed path. In order to avoid working with piecewise linear functions, our approach uses a series of parametric residual networks defined for successive subintervals of the parameter values where the ...

Routing messages in a network is often based on the assumption that each link, and so each path, in the network is bidirectional. The two directions of a path are employed in routing messages as follows. One direction is used by the nodes in the path to forward messages to their destination at the end of the path, and the other direction is used by the destination to inform the nodes in the pat...

We study the directed minimum latency problem: given an n-vertex asymmetric metric (V, d) with a root vertex r ∈ V , find a spanning path originating at r that minimizes the sum of latencies at all vertices (the latency of any vertex v ∈ V is the distance from r to v along the path). This problem has been well-studied on symmetric metrics, and the best known approximation guarantee is 3.59 [3]....

In this article, we study the problem of finding the next-to-shortest path in circular-arc graph. A next-to-shortest path between any pair of vertices in a shortest path amongst all paths between those vertices with length strictly greater than the length of the shortest path. The next-to-shortest path problem in a directed graph in NP-hard. Here we deigned a polynomial time algorithm to solve ...

Given a graph H, the size Ramsey number re(H, q) is the minimal number m for which there is a graph G with m edges such that every q-coloring of G contains a monochromatic copy of H. We study the size Ramsey number of the directed path of length n in oriented graphs, where no antiparallel edges are allowed. We give nearly tight bounds for every fixed number of colors, showing that for every q ≥...

In this paper, we show that Bandwidth is hard for the complexity class W[t] all \(t\in \mathbf{N}\), even caterpillars with hair length at most three. As intermediate problem, introduce Weighted Path Emulation problem: given a vertex-weighted path \(P_N\) and integer M, decide if there exists mapping of vertices to \(P_M\), such adjacent are mapped or equal vertices, total weight pre-image vert...

Let G be a plane bipartite graph. The Z-transformation graph Z(G) and its orientation Z̃(G) on the maximum matchings of G are de1ned. If G has a perfect matching, Z(G) and Z̃(G) are the usual Z-transformation graph and digraph. If G has neither isolated vertices nor perfect matching, then Z(G) is not connected. This paper mainly shows that some basic results for Z-transformation graph (digraph) o...

An activity network is an acyclic graph with non-negative weights and with a unique source and destination. A project consisting of a set of activities and precedence relationships can be represented by an activity network and the mathematical analysis of the network provides useful information for managing the project. In a traditional activity network, it is assumed that an activity always be...

Most of pointed Hopf algebras of dimension p with large coradical are shown to be generalized path algebras. By the theory of generalized path algebras it is obtained that the representations, homological dimensions and radicals of these Hopf algebras. The relations between the radicals of path algebras and connectivity of directed graphs are given. 2000 Mathematics subject Classification: 16w3...

Directed s-t connectivity is the problem of detecting whether there is a path from vertex s to vertex t in a directed graph. We present the rst known deterministic sublinear space, polynomial time algorithm for directed s-t connectivity. For n-vertex graphs, our algorithm can use as little as n=2 ( p logn) space while still running in polynomial time.