Daniel Olejár

An improved interval routing scheme for almost all networks based on dominating cliques

Motivated by the peer-to-peer content sharing systems in large-scale networks, we will study interval routing schemes in Erdos-Renyi random graphs. C. Gavoille and D. Peleg [13] posed an open question of whether almost all networks support a shortest-path interval routing scheme with 1 interval. In this paper, we answer this question partially by proving that in almost all networks, there is an interval routing scheme with 1 interval up to additive stretch 2. Our proof is based on the properties of dominating cliques in random graphs.

A detailed study of the dominating cliques phase transition in random graphs

A subset of nodes S ⊆V of a graph G =(V , E ) is a dominating clique if S is a dominating set and a clique of G . The phase transition of dominating cliques in Erdos-Renyi random graph model is investigated in this paper. Lower and upper bounds on the edge probability p for the existence of an r -node dominating clique are established in this paper. We prove therein that given an n -node random graph G from for r =c log1/p n with 1≤c ≤2 it holds: (1) if p >1/2 then an r -clique is dominating in G with a high probability and, (2) if

Integrity testing in WWW environment

p \leq ( 3 - \sqrt{5})/2

Weaknesses in EHA Authentication and Key Distribution Protocol

then an r -clique is not dominating in G with a high probability. The remaining range of the probability p is discussed with more attention. Within such a range, we provide intervals of r where a dominating clique existence probability is zero, positive but less than one, and one, respectively.

On Cryptographic Properties of Random Boolean Functions.

The successful growth of Internet, lead to application of World Wide Web (WWW) technologies in current IT systems. One of the traditional high-level objectives of IT security is integrity. We focus our attention on integrity in the WWW environment. We outline content and context of integrity testing as well as specific problems that need to be solved. Most of our attention is devoted, in a separate section, to heuristic approach to integrity testing.

On the order and the number of cliques in a random graph

Recently, there was a new authentication and key distribution protocol presented in [EHA98]. In this paper we show that certain claims on its properties are not valid. We also suggest some modifications to strengthen this protocol.