A 1984 problem of S. Z. Ditor asks whether there exists a lattice of cardinality א2, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martin’s Axiom restricted to collections of א1 dense subsets in posets of ...

In their 2009 paper, Corneil et al. design a linear time interval graph recognition algorithm based on six sweeps of Lexicographic Breadth-First Search (LBFS) and prove its correctness. They believe that their corresponding 5-sweep LBFS interval graph recognition algorithm is also correct. Thanks to the LBFS structure theory established mainly by Corneil et al., we are able to present a 4-sweep...

Recently lexicographic breadth first search (LexBFS) has been shown to be a very powerful tool for the development of linear time, easily implementable recognition algorithms for various families of graphs. In this paper, we add to this work by producing a simple two LexBFS sweep algorithm to recognize the family of cographs. This algorithm extends to other related graph families such as P4-red...

Misconceptions about the nature of the computing disciplines pose a serious problem to university faculties that offer computing degrees, as students enrolling on their programmes may come to realise that their expectations are not met by reality. This frequently results in the students’ early disengagement from the subject of their degrees which in turn can lead to excessive ‘wastage’, i.e. re...

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Today, event logs contain vast amounts of data that can easily overwhelm a human. Therefore, the mining of frequent patterns from event logs is an important system and network management task. This paper discusses the properties of event log data, analyses the suitability of popular mining algorithms for processing event log data, and proposes an efficient algorithm for mining frequent patterns...