Incremental 22-Edge-Connectivity in Directed Graphs

In this paper, we initiate the study of the dynamic maintenance of $2$-edge-connectivity relationships in directed graphs. We present an algorithm that can update the $2$-edge-connected blocks of a directed graph with $n$ vertices through a sequence of $m$ edge insertions in a total of $O(mn)$ time. After each insertion, we can answer the following queries in asymptotically optimal time: (i) Test in constant time if two query vertices $v$ and $w$ are $2$-edge-connected. Moreover, if $v$ and $w$ are not $2$-edge-connected, we can produce in constant time a "witness" of this property, by exhibiting an edge that is contained in all paths from $v$ to $w$ or in all paths from $w$ to $v$. (ii) Report in $O(n)$ time all the $2$-edge-connected blocks of $G$. To the best of our knowledge, this is the first dynamic algorithm for $2$-connectivity problems on directed graphs, and it matches the best known bounds for simpler problems, such as incremental transitive closure.Comment: Full version of paper presented at ICALP 201

GRAAL - A graph algorithmic language

FORTRAN-based version, FGRAAL, of graph algorithmic language GRAA

Surface networks

© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou

Efficient algorithms for a class of partitioning problems

The problem of optimally partitioning the modules of chain- or tree-like tasks over chain-structured or host-satellite multiple computer systems is addressed. This important class of problems includes many signal processing and industrial control applications. Prior research has resulted in a succession of faster exact and approximate algorithms for these problems. Polynomial exact and approximate algorithms are described for this class that are better than any of the previously reported algorithms. The approach is based on a preprocessing step that condenses the given chain or tree structured task into a monotonic chain or tree. The partitioning of this monotonic take can then be carried out using fast search techniques

Implementation of the Combined--Nonlinear Condensation Transformation

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of importance in linguistics, statistical-mechanics theory, and biophysics (statistical analysis of DNA sequences). We also discuss applications of the transformation in experimental mathematics, and we briefly expand on further applications in theoretical physics. Finally, we discuss a related Mathematica program for the computation of Lerch's transcendent.Comment: 23 pages, 1 table, 1 figure (Comput. Phys. Commun., in press