Nikola S. Nikolov

GEOMI: GEOmetry for maximum insight

This paper describes the GEOMI system, a visual analysis tool for the visualisation and analysis of large and complex networks. GEOMI provides a collection of network analysis methods, graph layout algorithms and several graph navigation and interaction methods. GEOMI is part of a new generation of visual analysis tools combining graph visualisation techniques with network analysis methods. GEOMI is available from http://www.cs.usyd.edu.au/~visual/valacon/geomi/.

How to Layer a Directed Acyclic Graph

We consider the problem of partitioning a directed acyclic graph into layers such that all edges point unidirectionally. We perform an experimental analysis of some of the existing layering algorithms and then propose a new algorithm that is more realistic in the sense that it is possible to incorporate specific information about node and edge widths into the algorithm. The goal is to minimize the total sum of edge spans subject to dimension constraints on the drawing. We also present some preliminary results from experiments we have conducted using our layering algorithm on over 5900 example directed acyclic graphs.

Graph layering by promotion of nodes

This work contributes to the wide research area of visualization of hierarchical graphs. We present a new polynomial-time heuristic which can be integrated into the Sugiyama method for drawing hierarchical graphs. Our heuristic, which we call Promote Layering (PL), is applied to the output of the layering phase of the Sugiyama method. PL is a simple and easy to implement algorithm which decreases the number of so-called dummy (or virtual) nodes in a layered directed acyclic graph. In particular, we propose applying PL after the longest-path layering algorithm and we present an extensive empirical evaluation of this layering technique.

Visualization and analysis of email networks

This paper presents various methods for visualization and analysis of email networks; visualization on the surface of a sphere to reveal communication patterns between different groups, a hierarchical drawing displaying the centrality analysis of nodes to emphasize important nodes, a 2.5D visualization for temporal email networks to analyze the evolution of email relationships changing over time, and an ambient display for finding social circles derived from the email network. Each method was evaluated with various data sets from a research organization. We also extended our method for visual analysis of an email virus network.

Hierarchical layouts of directed graphs in three dimensions

We introduce a new graph drawing convention for 3D hierarchical drawings of directed graphs. The vertex set is partitioned into layers of vertices drawn in parallel planes. The vertex set is further partitioned into k ≥ 2 subsets, called walls. The layout consists of a set of parallel walls which are perpendicular to the set of parallel planes of the layers. We also outline a method for computing such layouts and introduce four alternative algorithms for partitioning the vertex set into walls which address different aesthetic requirements.

In search for efficient heuristics for minimum-width graph layering with consideration of dummy nodes

We propose two fast heuristics for solving the NP-hard problem of graph layering with the minimum width and consideration of dummy nodes. Our heuristics can be used at the layer-assignment phase of the Sugiyama method for drawing of directed graphs. We evaluate our heuristics by comparing them to the widely used fast-layering algorithms in an extensive computational study with nearly 6000 input graphs. We also demonstrate how the well-known longest-path and Coffman--Graham algorithms can be used for finding narrow layerings with acceptable aesthetic properties.

A Branch-and-Cut Approach to the Directed Acyclic Graph Layering Problem

We consider the problem of layering Directed Acyclic Graphs, an NP-hard problem. We show that some useful variants of the problem are also NP-hard. We provide an Integer Linear Programming formulation of a generalization of the standard problem and discuss how a branch-and-bound algorithm could be improved upon with cutting planes. We then describe a separation algorithm for two classes of valid inequalities that we have identified - one of which is facet-defining - and discuss their efficacy.

A 2.5D Hierarchical Drawing of Directed Graphs

We introduce a new graph drawing convention for 2.5D hierarchical drawings of directed graphs. The vertex set is partitioned both into layers of vertices drawn in parallel planes and into k � 2 subsets, called walls, and also drawn in parallel planes. The planes of the walls are perpendicular to the planes of the layers. We present a method for computing such layouts and introduce five alternative algorithms for partitioning the vertex set into walls which correspond to different aesthetic requirements. We evaluate our method with an extensive computational study. 1

Evolving Smart Initial Layouts for Force-Directed Graph Drawing

We propose a genetic algorithm (GA) for solving the maximization version of the Optimal Linear Arrangement problem and we also demonstrate how solutions found by it can be used for constructing smart initial layouts for force-directed graph drawing. Effectively, we show that our GA can be used as a first step in force-directed graph drawing for achieving more aesthetically pleasing graph layouts at the end. We present experimental results which show that the initial layouts based on the solutions of our GA reduce the number of edge crossings in force-directed graph layouts.

Applying Ant Colony Optimization Metaheuristic to the DAG Layering Problem

This paper presents the design and implementation of an ant colony optimization based algorithm for solving the DAG layering problem. This algorithm produces compact layerings by minimising their width and height. Importantly it takes into account the contribution of dummy vertices to the width of the resulting layering.