Motivated by a recent paper by Cichoń and Macyna [1], who introduced m counters (instead of just one) in the approximate counting scheme first analysed by Flajolet [2], we analyse the moments of the sum of the m counters, using techniques that proved to be successful already in several other contexts [11].

vi Chapter 1 Three Algorithmic Concerns 1 1.

We do a probabilistic analysis of the problem of distributing a single piece of information to the vertices of a graph G. Assuming that the input graph G is Gn,p, we prove an O(lnn/n) upper bound on the edge density needed so that with high probability the information can be broadcast in ⌈log2 n⌉ rounds.

Influenza is one of the most common and severe diseases worldwide. Devastating epidemics actuated by a new subtype of the influenza A virus occur again and again with the most important example given by the Spanish Flu in 1918/19 with more than 27 million deaths. For the development of pandemic plans it is essential to understand the character of the dissemination of the disease. We employ an e...

We study a leader election protocol that we call the Swedish leader election protocol. This name comes from a protocol presented by L. Bondesson, T. Nilsson, and G. Wikstrand (2007). The goal is to select one among n > 0 players, by proceeding through a number of rounds. If there is only one player remaining, the protocol stops and the player is declared the leader. Otherwise, all remaining pla...

Abstract. In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily without resorting to complex analysis techniques as it is usually the case. This approach gives a unified probabilistic treatment of these questions. ...

This paper shows that we can take advantage of information about the probabilities of the occurrences of events, when this information is available, to refine the classical results of diagnosability: instead of giving a binary answer, the approach we propose allows one to quantify, in particular, the degree of non-diagnosability in case of negative answer. The dynamics of the system is modelled...