Dimitris Sakavalas

Reliable Broadcast with Respect to Topology Knowledge

We study the Reliable Broadcast problem in incomplete networks against a Byzantine adversary. We examine the problem under the locally bounded adversary model of Koo (2004) and the general adversary model of Hirt and Maurer (1997) and explore the tradeoff between the level of topology knowledge and the solvability of the problem.

A Graph Parameter That Matches the Resilience of the Certified Propagation Algorithm

We consider the Secure Broadcast problem in incomplete networks. We study the resilience of the Certified Propagation Algorithm (CPA), which is particularly suitable for ad hoc networks. We address the issue of determining the maximum number of corrupted players \(t^{\rm CPA}_{\rm max}\) that CPA can tolerate under the t-locally bounded adversary model, in which the adversary may corrupt at most t players in each player’s neighborhood. For any graph G and dealer-node D we provide upper and lower bounds on \(t^{\rm CPA}_{\rm max}\) that can be efficiently computed in terms of a graph theoretic parameter that we introduce in this work. Along the way we obtain an efficient 2-approximation algorithm for \(t^{\rm CPA}_{\rm max}\). We further introduce two more graph parameters, one of which matches \(t^{\rm CPA}_{\rm max}\) exactly.

Reliable Communication via Semilattice Properties of Partial Knowledge

A fundamental primitive in distributed computing is Reliable Message Transmission (RMT), which refers to the task of correctly sending a message from a party to another, despite the presence of Byzantine corruptions. We explicitly consider the initial knowledge possessed by the parties-players by employing the recently introduced Partial Knowledge Model [13], where a player has knowledge over an arbitrary subgraph of the network, and the general adversary model of Hirt and Maurer [5]. Our main contribution is a tight condition for the feasibility of RMT in the setting resulting from the combination of these two quite general models; this settles the central open question of [13].

Energy-efficient broadcasting in ad hoc wireless networks

Abstract We study energy-efficient broadcasting in wireless networks of unknown topology (ad hoc). We measure energy efficiency by the maximum number of transmissions (‘shots’) allowed to any node in the network. In particular, we examine the case in which a bound k is given and a node may transmit at most k times during the broadcasting protocol. Initially, we focus on oblivious algorithms for k-shot broadcasting, that is, algorithms where at each step each node decides whether to transmit or not with no consideration of the transmission history. Our main contributions are (a) a lower bound of Ω ( n 2 / k ) on the broadcasting time of any oblivious k-shot broadcasting algorithm, and (b) an oblivious broadcasting protocol that achieves a matching upper bound, namely O ( n 2 / k ) , for every k ≤ n and an upper bound of O ( n 3 / 2 ) for every k > n . We also study the general case of adaptive broadcasting protocols where nodes decide whether to transmit based on all the available information, namely the transmission history known to each. We prove a lower bound of Ω ( n 1 + k k ) on the broadcasting time of any protocol by introducing the transmission tree construction which generalizes previous approaches.

Reliable broadcast with respect to topology knowledge

We study the Reliable Broadcast problem in incomplete networks against a Byzantine adversary. We examine the problem under the locally bounded adversary model of Koo (Proceedings of the 23rd annual ACM symposium on principles of distributed computing, PODC ’04, St. John’s, Newfoundland, Canada, 25–28 July 2004, ACM New York pp 275–282, 2004) and the general adversary model of Hirt and Maurer (Proceedings of the 16th annual ACM symposium on principles of distributed computing, PODC ’97, Santa Barbara, California, USA, August 21–24, 1997 ACM, New York pp 25–34, 1997) and explore the tradeoff between the level of topology knowledge and the solvability of the problem. In order to explore this tradeoff we introduce the partial knowledge model which captures the situation where each player has arbitrary topology knowledge. We refine the local pair-cut technique of Pelc and Peleg (Inf Process Lett 93(3):109–115, 2005) in order to obtain impossibility results for every level of topology knowledge and any type of corruption distribution. On the positive side we devise protocols that match the obtained bounds, and thus, exactly characterize the classes of graphs in which Reliable Broadcast is possible. Among others, we show that Koo’s Certified Propagation Algorithm (CPA) is unique, against locally bounded adversaries in ad hoc networks, among all safe algorithms, i.e., algorithms which never cause a node to decide on an incorrect value. This means that CPA can tolerate as many local corruptions as any other safe algorithm; this settles an open question posed by Pelc and Peleg. We also provide an adaptation of CPA achieving reliable broadcast against general adversaries and prove that this algorithm too is unique under this model. To the best of our knowledge this is the first optimal algorithm for Reliable Broadcast in generic topology ad hoc networks against general adversaries.

The Byzantine Generals Problem in Generic and Wireless Networks

In this chapter we consider the design of Secure Broadcast protocols in generic networks of known topology. Studying the problem of Secure Message Transmission (SMT) proves essential for achieving Broadcast in incomplete networks. We present a polynomial protocol that achieves parallel secure message transmissions between any two sets of nodes of an incomplete network provided that the weakest connectivity conditions which render the Broadcast problem solvable hold. Using the above, we show that the SMT protocol can be used as a subroutine for the simulation of any known protocol for complete networks, which leads us to protocols for generic networks which remain polynomial with respect to the measures of consideration. We extend our result to the case of wireless networks by exploiting the fact that participants are committed to perform local broadcasts, which greatly facilitates achieving an agreement.