We present the first streaming algorithm for the longest path problem in undirected graphs. The input graph is given as a stream of edges and RAM is limited to only a linear number of edges at a time (linear in the number of vertices n). We prove a per-edge processing time of O(n), where a naive solution would have required Ω(n2). Moreover, we give a concrete linear upper bound on the number of...

We present a statistical path loss model derived from 1.9 GHz experimental data collected across the United States in 95 existing macrocells. The model is for suburban areas, and it distinguishes between different terrain categories. Moreover, it applies to distances and base antenna heights not well-covered by existing models. The characterization used is a linear curve fitting the decibel pat...

Failure of even a single fiber link in DWDM mesh networks can cause severe data and revenue loss due to failure of several lightpaths of high bandwidth. This paper investigates this problem using shared path protection technique. First, we propose a link disjoint path finding heuristic, Multiple Active Path Search (MAPS) and show that it works even under trap topologies where conventional algor...

We consider weighted path lengths to the extremal leaves in a random binary search tree. When linearly scaled, the weighted path length to the minimal label has Dickman’s infinitely divisible distribution as a limit. By contrast, the weighted path length to the maximal label needs to be centered and scaled to converge to a standard normal variate in distribution. The exercise shows that path le...

The present letter gives a rigorous way from quantum to classical random walks by introducing an independent random fluctuation and then taking expectations based on a path integral approach.

When are we locked in a path? This is one of the main questions concerning path dependency. Coming from Arthur's model of increasing returns and technology adoption (Arthur 1989), this paper addresses the question of when and how a lock-in occurs. To gain a better understanding of the path process, different modifications are made. First, the random selection of two types of adopters is substit...

Secure communication is a necessity for some wireless sensor network (WSN) applications. However, the resource constraints of a sensor render existing cryptographic systems for traditional network systems impractical for a WSN. Random key predistribution scheme has been proposed to overcome these limits. In this scheme, a ring of keys is randomly drawn from a large key pool and assigned to a se...

Robustness of ecological flow networks under random failure of arcs is considered with respect to two different functionalities: coherence and circulation. In our previous work, we showed that each functionality is associated with a natural path notion: lateral path for the former and directed path for the latter. Robustness of a network is measured in terms of the size of the giant laterally c...

We present an improved SPFA algorithm for the single source shortest path problem. For a random graph, the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network. SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed. In the improved SPFA, MinPoP principle is employed to improve the quality of the qu...