We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...

We present a new probabilistic technique of embedding graphs in Z, the d-dimensional integer lattice, in order to find the shortest paths and shortest distances between pairs of nodes. In our method the nodes of a breath first search (BFS) tree, starting at a particular node, are labeled as the sites found by a branching random walk on Z. After describing a greedy algorithm for routing (distanc...

Solving fundamental graph problems, such as shortest paths, minimum cut and maximum flow, on distributed networks (in the so-called CONGEST model) is a central question in distributed computing. By allowing approximate solutions, rapid progress has been made in recent years resulting in tight algorithms and lower bounds in many cases. However, pretty much nothing is known for solving many of th...

Routing in wireless ad hoc networks of mobile nodes is complicated by the fact that the transmission ranges and the communication bandwidth is limited, and that the network topology is highly dynamic due to continuously moving nodes. In this paper, a new approach is presented to equip proactive distance-vector routing algrithms with the capability of using multiple paths to each target. The bas...

In this paper, we propose a new path-based multicast algorithm that is called Row/Column-First algorithm. The proposed algorithm constructs a set of multicast paths to deliver a multicast message to all multicast destination nodes. The set of multicast paths are all of row-first or column-first subcategories to maximize the multicast performance. The selection of row-first or column-first appro...

We study the communication of quantum information in networks of (directed) quantum channels. We consider the asymptotic rates of high fidelity quantum communication between specific sender-receiver pairs, and obtain outer and inner bounds of the achievable rate regions. All four scenarios of classical communication assistance (none, forward, backward, and two-way) are considered. For networks ...

This work develops a generic framework, called the bag-of-paths (BoP), for link and network data analysis. The central idea is to assign a probability distribution on the set of all paths in a network. More precisely, a Gibbs-Boltzmann distribution is defined over a bag of paths in a network, that is, on a representation that considers all paths independently. We show that, under this distribut...