Evangelos Kranakis

Random Constraint Satisfaction: A More Accurate Picture

In the last few years there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Quite intriguingly, experimental results with various models for generating random CSP instances suggest that the probability of such problems having a solution exhibits a “threshold–like” behavior. In this spirit, some preliminary theoretical work has been done in analyzing these models asymptotically, i.e., as the number of variables grows. In this paper we prove that, contrary to beliefs based on experimental evidence, the models commonly used for generating random CSP instances do not have an asymptotic threshold. In particular, we prove that asymptotically almost all instances they generate are overconstrained, suffering from trivial, local inconsistencies. To complement this result we present an alternative, single–parameter model for generating random CSP instances and prove that, unlike current models, it exhibits non–trivial asymptotic behavior. Moreover, for this new model we derive explicit bounds for the narrow region within which the probability of having a solution changes dramatically.

Approximating the unsatisfiability threshold of random formulas

Let f be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number k such that if the ratio of the number of clauses over the number of variables of f strictly exceeds k , then f is almost certainly unsatisfiable. By a well-known and more or less straightforward argument, it can be shown that kF5.191. This upper bound was improved by Kamath et al. to 4.758 by first providing new improved bounds for the occupancy problem. There is strong experimental evidence that the value of k is around 4.2. In this work, we define, in terms of the random formula f, a decreasing sequence of random variables such that, if the expected value of any one of them converges to zero, then f is almost certainly unsatisfiable. By letting the expected value of the first term of the sequence converge to zero, we obtain, by simple and elementary computations, an upper bound for k equal to 4.667. From the expected value of the second term of the sequence, we get the value 4.601q . In general, by letting the U This work was performed while the first author was visiting the School of Computer Science, Carleton Ž University, and was partially supported by NSERC Natural Sciences and Engineering Research Council . of Canada , and by a grant from the University of Patras for sabbatical leaves. The second and third Ž authors were supported in part by grants from NSERC Natural Sciences and Engineering Research . Council of Canada . During the last stages of this research, the first and last authors were also partially Ž . supported by EU ESPRIT Long-Term Research Project ALCOM-IT Project No. 20244 . †An extended abstract of this paper was published in the Proceedings of the Fourth Annual European Ž Symposium on Algorithms, ESA’96, September 25]27, 1996, Barcelona, Spain Springer-Verlag, LNCS, . pp. 27]38 . That extended abstract was coauthored by the first three authors of the present paper. Correspondence to: L. M. Kirousis Q 1998 John Wiley & Sons, Inc. CCC 1042-9832r98r030253-17 253

Asynchronous deterministic rendezvous in graphs

Two mobile agents (robots) having distinct labels and located in nodes of an unknown anonymous connected graph have to meet. We consider the asynchronous version of this well-studied rendezvous problem and we seek fast deterministic algorithms for it. Since in the asynchronous setting, meeting at a node, which is normally required in rendezvous, is in general impossible, we relax the demand by allowing meeting of the agents inside an edge as well. The measure of performance of a rendezvous algorithm is its cost: for a given initial location of agents in a graph, this is the number of edge traversals of both agents until rendezvous is achieved. If agents are initially situated at a distance D in an infinite line, we show a rendezvous algorithm with cost O(D|Lmin|2) when D is known and O((D + |Lmax|)3) if D is unknown, where |Lmin| and |Lmax| are the lengths of the shorter and longer label of the agents, respectively. These results still hold for the case of the ring of unknown size, but then we also give an optimal algorithm of cost O(n|Lmin|), if the size n of the ring is known, and of cost O(n|Lmax|), if it is unknown. For arbitrary graphs, we show that rendezvous is feasible if an upper bound on the size of the graph is known and we give an optimal algorithm of cost O(D|Lmin|) if the topology of the graph and the initial positions are known to agents.

On the false-positive rate of Bloom filters

Bloom filters are a randomized data structure for membership queries dating back to 1970. Bloom filters sometimes give erroneous answers to queries, called false positives. Bloom analyzed the probability of such erroneous answers, called the false-positive rate, and Blooms analysis has appeared in many publications throughout the years. We show that Blooms analysis is incorrect and give a correct analysis.

On interdomain routing security and pretty secure BGP (psBGP)

It is well known that the Border Gateway Protocol (BGP), the IETF standard interdomain routing protocol, is vulnerable to a variety of attacks, and that a single misconfigured or malicious BGP speaker could result in large-scale service disruption. In this paper, we present Pretty Secure BGP (psBGP)---a proposal for securing BGP, including an architectural overview, design details for significant aspects, and preliminary security and operational analysis. psBGP differs from other security proposals (e.g., S-BGP and soBGP) in that it makes use of a single-level PKI for AS number authentication, a decentralized trust model for verifying the propriety of IP prefix origin, and a rating-based stepwise approach for AS_PATH (integrity) verification. psBGP trades off the strong security guarantees of S-BGP for presumed-simpler operation, e.g., using a PKI with a simple structure, with a small number of certificate types, and of manageable size. psBGP is designed to successfully defend against various (nonmalicious and malicious) threats from uncoordinated BGP speakers, and to be incrementally deployed with incremental benefits.

Fault-Tolerant Broadcasting in Radio Networks

We consider broadcasting in radio networks that are subject to permanent node failures of unknown location. Nodes are spread in a region in some regular way. We consider two cases: nodes are either situated at integer points of a line or they are situated on the plane, at grid points of a square or hexagonal mesh. Nodes send messages in synchronous time slots. Each node v has a given transmission range of the same radius R. All nodes located within this range can receive messages from v. However, a node situated in the range of two or more nodes that send messages simultaneously, cannot receive these messages and hears only noise. Faulty nodes do not receive or send any messages. We give broadcasting algorithms whose worst-case running time has optimal order of magnitude, and we prove corresponding lower bounds. In case of nonadaptive algorithms this order of magnitude is θ(D + t), and for adaptive algorithms it is Θ(D + log(min(R, t))), where t is an upper bound on the number of faults in the network and D is the diameter of the fault-free part of the network that can be reached from the source as a result of those faults.

Detecting impersonation attacks in future wireless and mobile networks

Impersonation attacks in wireless and mobile networks by professional criminal groups are becoming more sophisticated. We confirm with simple risk analysis that impersonation attacks offer attractive incentives to malicious criminals and should therefore be given highest priority in research studies. We also survey our recent investigations on Radio Frequency Fingerprinting and User Mobility Profiles and discuss details of our methodologies for building enhanced intrusion detection systems for future wireless and mobile networks.

Power consumption in packet radio networks

In this paper we study the problem of assigning transmission ranges to the nodes of a multi-hop packet radio network so as to minimize the total power consumed under the constraint that adequate power is provided to the nodes to ensure that the network is strongly connected (i.e., each node can communicate along some path in the network to every other node). Such assignment of transmission ranges is called complete. We also consider the problem of achieving strongly connected bounded diameter networks.

Resisting Malicious Packet Dropping in Wireless Ad Hoc Networks

Most of the routing protocols in wireless ad hoc networks, such as DSR, assume nodes are trustworthy and cooperative. This assumption renders wireless ad hoc networks vulnerable to various types of Denial of Service (DoS) attacks. We present a distributed probing technique to detect and mitigate one type of DoS attacks, namely malicious packet dropping, in wireless ad hoc networks. A malicious node can promise to forward packets but in fact fails to do so. In our distributed probing technique, every node in the network will probe the other nodes periodically to detect if any of them fail to perform the forwarding function. Subsequently, node state information can be utilized by the routing protocol to bypass those malicious nodes. Our experiments show that in a moderately changing network, the probing technique can detect most of the malicious nodes with a relatively low false positive rate. The packet delivery rate in the network can also be increased accordingly.

Boolean functions and computation models

1. Boolean Functions and Circuits.- 2. Circuit Lower Bounds.- 3. Circuit Upper Bounds.- 4. Randomness and Satisfiability.- 5. Propositional Proof Systems.- 6. Machine Models and Function Algebras.- 7. Higher Types.- References.