Ludek Kucera

Algorithm Animation for Teaching

We give an overview of rules and techniques to create a good algorithm animation, with emphasis on animations that would be used when teaching algorithms. In this context, we propose that animations should in particular emphasize the visualization of correctness invariants and the complexity of the algorithms. This implies that writing a good animation must be more than just showing the graphically enhanced runtime debugging provided by most common animation systems; instead, each animation must be individually designed and programmed.

On learning monotone DNF formulae under uniform distributions

Abstract We show how to learn in polynomial time monotone d-term DNF formulae (formulae in disjunctive normal form with at most d terms) using positive examples drawn from a distribution that is a generalization of the uniform distribution.

Correlation Model of Worm Propagation on Scale-Free Networks

The problem of network worms is worsening despite increasing efforts and expenditure on cyber-security. Worm propagation is a random process that creates a complex system of interacting agents (worm copies) over the propagation medium – a scale-free graph, representing real-world networks. Understanding the propagation of network worms on scale-free graphs is the first step towards devising effective techniques for worm quarantining. After presenting the drawbacks of existing mean-field models, we develop a pair-approximation (correlation) model of worm propagation that employs the salient network characteristics – order, size, degree distribution, and transitivity. Inclusion of the transitivity shows significant improvement over existing pair-approximation models. The validity of the model is confirmed by comparing the numeric solution of the model to results from our individual-based simulation. Our model demonstrates that the network structure has considerable impact on the propagation dynamics when the worm uses local propagation strategies.

Efficient Distributed Algorithms for Dynamic Access to Shared Multiuser Channels in SINR-Constrained Wireless Networks

In wireless networks, simultaneously active transmitters typically operate in separate communication channels to avoid mutual interference. This study focuses on the challenge of increasing the capacity of a wireless network by enabling multiple transmissions in each available channel. Active transmitters are assumed to maintain the receiver signal-to-noise-and-interference ratio (SINR) at a predetermined target value via power control to promote the quality of wireless connections. To this end, we propose distributed medium access algorithms that allow every transmitter-receiver pair to determine whether a target SINR is physically achievable through iterative power control in a given shared channel. The proposed algorithms are shown by theoretical analysis to be fast, accurate, and energy efficient. Numerical simulations demonstrate their ability to outperform related medium access schemes based on random access, carrier sensing, controlled power up, or invariant channel probing. Our major contribution consists of solving the open problem of accurate real-time computation of the spectral radius of an unknown network information matrix. This makes our framework applicable not only to testing target SINR achievability, but also to other aspects of wireless engineering such as energy efficiency, power control stability, and handover prioritization, in which knowledge of the spectral radius plays a key role.

On the expected performance of a parallel algorithm for finding maximal independent subsets of a random graph

We consider the parallel greedy algorithm of Coppersmith, Raghavan, and Tompa (Proc. of 28th Annual IEEE Symp. on Foundations of Computer Science, pp. 260–269, 1987) for finding the lexicographically first maximal independent set of a graph. We prove an Ω(log n) bound on the expected number of iterations for most edge densities. This complements the O(log n) bound proved in Calkin and Frieze (Random Structures and Algorithms, Vol. 1, pp. 39–50, 1990).

Optimum Allocation of Energy and Spectrum in Power-Controlled Wireless Networks with QoS Constraints

An important performance measure in wireless networks is the manner in which the network can distributively manage its limited energy and spectrum resources, while assuring certain quality of service for communicating users. The current practice is to develop schemes with low complexity that are based on workable, but theoretically suboptimal techniques such as random access or carrier sensing. To address the need for equally simple, but optimally performing resource management schemes, we propose a set of optimum distributed algorithms for adaptive admission control and power control, which jointly (i) maximize the number of transmitters that transmit simultaneously in shared channel(s) with a guaranteed target signal-to-interference and noise ratio (SINR) at the receiver; (ii) minimize the transmit powers required to satisfy the SINR targets; (iii) use interference measurements as the only decision-making input; and (iv) provide inadmissible links with feedback on feasible SINR for (re)admission purposes. Unlike previous studies in which SINR targets were assumed as constants, we defined these targets using arbitrary linear functions of interference. From numerical simulations, it is confirmed that the proposed scheme outperforms other schemes by achieving the theoretical performance bounds.

Visualisation of algorithms

The present paper summarises the authors experience in teaching algorithms in undergraduate courses for students of Informatics at Charles University. In the authors view, the most efficient way of instruction is a classical lecture in a lecture hall that guarantees the quality of contact between a teacher and a student, that cannot be matched by any audiovisual channel; but with a teacher supported by a complex visualisation environment made to requirements of a particular algorithm, which not only animates the algorithm (forward and backward computation with or without interruptions), but also makes it possible to display the information necessary for understanding and analysing the algorithm (e.g., invariants of correctness, termination and complexity analysis, complexity related features etc.), implementation details and other important topics. Certain aspects of such visualisation environments are discussed.

Wait-free deflection routing of long messages

In order to obtain the lowest possible latency, routing algorithms should try to avoid a message waiting for resources (network links) blocked by other messages or multiplexing of more messages over one physical channel. This requirement becomes especially important in the case of long messages. The only type of protocols able to guarantee waiting free routing under heavy load are algorithms based on deflection (also called nonminimal adaptive or hot potato) routing. This paper deals with problems connected with the use of deflection algorithms. In contrast to the case of nonadaptive or partially (e.g., minimal) adaptive routing, it is very infrequent that an unrestricted deflection routing becomes deadlocked and, similarly, livelock is not a serious problem. On the other hand, there is another phenomenon, called a deflection jam, that limits throughput of deflection algorithms used to route long messages. It has been observed for many deflection heuristics, interconnection network topologies, and both virtual cut-through and wormhole routing. A deflection jam is a sudden and persistent saturation of a network which sometimes occur, after a very long period of undisturbed communication. This paper describes events that trigger this saturation which suggest ways to design improved and stable deflection routing algorithms.