Tomasz Radzik

Shortest paths algorithms: theory and experimental evaluation

We conduct an extensive computational study of shortest paths algorithms, including some very recent algorithms. We also suggest new algorithms motivated by the experimental results and prove interesting theoretical results suggested by the experimental data. Our computational study is based on several natural problem classes which identify strengths and weaknesses of various algorithms. These problem classes and algorithm implementations form an environment for testing the performance of shortest paths algorithms. The interaction between the experimental evaluation of algorithm behavior and the theoretical analysis of algorithm performance plays an important role in our research.

The cover times of random walks on hypergraphs

Random walks in graphs have been applied to various network exploration and network maintenance problems. In some applications, however, it may be more natural, and more accurate, to model the underlying network not as a graph but as a hypergraph, and solutions based on random walks require a notion of random walks in hypergraphs. At each step, a random walk on a hypergraph moves from its current position v to a random vertex in a randomly selected hyperedge containing v. We consider two definitions of cover time of a hypergraph H. If the walk sees only the vertices it moves between, then the usual definition of cover time, C(H), applies. If the walk sees the complete edge during the transition, then an alternative definition of cover time, the inform time I(H) is used. The notion of inform time models passive listening which fits the following types of situations. The particle is a rumor passing between friends, which is overheard by other friends present in the group at the same time. The particle is a message transmitted randomly from location to location by a directional transmission in an ad-hoc network, but all receivers within the transmission range can hear. In this paper we give an expression for C(H) which is tractable for many classes of hypergraphs, and calculate C(H) and I(H) exactly for random r-regular, s-uniform hypergraphs. We find that for such hypergraph whp C(H)/I(H) = Θ(s) for large s.

Multiple Random Walks in Random Regular Graphs

We study properties of multiple random walks on a graph under various assumptions of interaction between the particles. To give precise results, we make the analysis for random regular graphs. The cover time of a random walk on a random

Searching for black-hole faults in a network using multiple agents

r

Hardness and approximation results for Black Hole Search in arbitrary networks

-regular graph was studied in [C. Cooper and A. Frieze, SIAM J. Discrete Math., 18 (2005), pp. 728-740], where it was shown with high probability (whp) that for

Fast deterministic approximation for the multicommodity flow problem

r\geq3

Faster Deterministic Gossiping in Directed Ad Hoc Radio Networks

the cover time is asymptotic to

Fractional Combinatorial Optimization

\theta_r n\ln n

On the wake-up problem in radio networks

, where

Deterministic Communication in Radio Networks with Large Labels

\theta_r=(r-1)/(r-2)