Almost linear time operations with triangular sets

Building PQR trees in almost-linear time

In 1976, Booth and Leuker invented the PQ trees as a compact way of storing and manipulating all the permutations on n elements that keep consecutive the elements in certain given sets C1, C2, . . . , Cm. Such permutations are called valid. This problem finds applications in DNA physical mapping, interval graph recognition, logic circuit optimization and data retrieval, among others. PQ trees c...

Symbolic Program Analysis in Almost-Linear Time

Model sets, almost periodic patterns, uniform density and linear maps

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they are almost periodic patterns and thus possess a uniform density. In the second part, we prove that the class of model sets and almost periodic patterns are st...

Cardinalities of fuzzy sets with triangular norms

This paper presents a variety of cardinality concepts offered by cardinality theory of triangular norm-based fuzzy sets, including the scalar and the "fuzzy" streams.

Representing Sets with Sums of Triangular Numbers

We investigate here sums of triangular numbers f(x) := ∑