arXiv subjects

Antonios Symvonis

Publications and source records attributed to Antonios Symvonis.

32 records · Page 2Linked to original sources

arXiv2017

Planar Drawings of Fixed-Mobile Bigraphs

A fixed-mobile bigraph G is a bipartite graph such that the vertices of one partition set are given with fixed positions in the plane and the mobile vertices of the other part, together with the edges, must be added to the drawing. We assume that G is planar and study the problem of finding, for a given k >= 0, a planar poly-line drawing of G with at most k bends per edge. In the most general case, we show NP-hardness. For k=0 and under additional constraints on the positions of the fixed or mobile vertices, we either prove that the problem is polynomial-time solvable or prove that it belongs to NP. Finally, we present a polynomial-time testing algorithm for a certain type of "layered" 1-bend drawings.

cs.CG↗

arXiv2017

Rooted Uniform Monotone Minimum Spanning Trees

We study the construction of the minimum cost spanning geometric graph of a given rooted point set $P$ where each point of $P$ is connected to the root by a path that satisfies a given property. We focus on two properties, namely the monotonicity w.r.t. a single direction ($y$-monotonicity) and the monotonicity w.r.t. a single pair of orthogonal directions ($xy$-monotonicity). We propose algorithms that compute the rooted $y$-monotone ($xy$-monotone) minimum spanning tree of $P$ in $O(|P|\log^2 |P|)$ (resp. $O(|P|\log^3 |P|)$) time when the direction (resp. pair of orthogonal directions) of monotonicity is given, and in $O(|P|^2\log|P|)$ time when the optimum direction (resp. pair of orthogonal directions) has to be determined. We also give simple algorithms which, given a rooted connected geometric graph, decide if the root is connected to every other vertex by paths that are all monotone w.r.t. the same direction (pair of orthogonal directions).

cs.CG↗

arXiv2016

Low Ply Drawings of Trees

We consider the recently introduced model of \emph{low ply graph drawing}, in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The \emph{ply-disk} of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of ply-disks having a common overlap is called the \emph{ply-number} of the drawing. We focus on trees. We first consider drawings of trees with constant ply-number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic ply-number and show that trees with maximum degree $6$ always admit such drawings in polynomial area.

cs.DS↗

arXiv2013

A Fraud Detection Visualization System Utilizing Radial Drawings and Heat-maps

We present a prototype system developed in cooperation with a business organization that combines information visualization and pattern-matching techniques to detect fraudulent activity by employees. The system is built upon common fraud patterns searched while trying to detect occupational fraud suggested by internal auditors of a business company. The main visualization of the system consists of a multi-layer radial drawing that represents the activity of the employees and clients. Each layer represents a different examined pattern whereas heat-maps indicating suspicious activity are incorporated in the visualization. The data are first preprocessed based on a decision tree generated by the examined patterns and each employee is assigned a value indicating whether or not there exist indications of fraud. The visualization is presented as an animation and the employees are visualized one by one according to their severity values together with their related clients.

cs.OH↗

arXiv2013

Many-to-One Boundary Labeling with Backbones

In this paper we study \emph{many-to-one boundary labeling with backbone leaders}. In this new many-to-one model, a horizontal backbone reaches out of each label into the feature-enclosing rectangle. Feature points that need to be connected to this label are linked via vertical line segments to the backbone. We present dynamic programming algorithms for label number and total leader length minimization of crossing-free backbone labelings. When crossings are allowed, we aim to obtain solutions with the minimum number of crossings. This can be achieved efficiently in the case of fixed label order, however, in the case of flexible label order we show that minimizing the number of leader crossings is NP-hard.

cs.CG↗

arXiv2013

Occupational Fraud Detection Through Visualization

Occupational fraud affects many companies worldwide causing them economic loss and liability issues towards their customers and other involved entities. Detecting internal fraud in a company requires significant effort and, unfortunately cannot be entirely prevented. The internal auditors have to process a huge amount of data produced by diverse systems, which are in most cases in textual form, with little automated support. In this paper, we exploit the advantages of information visualization and present a system that aims to detect occupational fraud in systems which involve a pair of entities (e.g., an employee and a client) and periodic activity. The main visualization is based on a spiral system on which the events are drawn appropriately according to their time-stamp. Suspicious events are considered those which appear along the same radius or on close radii of the spiral. Before producing the visualization, the system ranks both involved entities according to the specifications of the internal auditor and generates a video file of the activity such that events with strong evidence of fraud appear first in the video. The system is also equipped with several different visualizations and mechanisms in order to meet the requirements of an internal fraud detection system.

cs.CY↗

arXiv2011

Upward Point Set Embeddability for Convex Point Sets is in $P$

In this paper, we present a polynomial dynamic programming algorithm that tests whether a $n$-vertex directed tree $T$ has an upward planar embedding into a convex point-set $S$ of size $n$. Further, we extend our approach to the class of outerplanar digraphs. This nontrivial and surprising result implies that any given digraph can be efficiently tested for an upward planar embedding into a given convex point set.

cs.DS↗

arXiv2011

Geometric Simultaneous RAC Drawings of Graphs

In this paper, we introduce and study "geometric simultaneous RAC drawing problems", i.e., a combination of problems on geometric RAC drawings and geometric simultaneous graph drawings. To the best of our knowledge, this is the first time where such a combination is attempted.

cs.DS↗

arXiv2010

Upward Point-Set Embeddability

We study the problem of Upward Point-Set Embeddability, that is the problem of deciding whether a given upward planar digraph $D$ has an upward planar embedding into a point set $S$. We show that any switch tree admits an upward planar straight-line embedding into any convex point set. For the class of $k$-switch trees, that is a generalization of switch trees (according to this definition a switch tree is a $1$-switch tree), we show that not every $k$-switch tree admits an upward planar straight-line embedding into any convex point set, for any $k \geq 2$. Finally we show that the problem of Upward Point-Set Embeddability is NP-complete.

cs.DS↗

arXiv2010

Maximizing the Total Resolution of Graphs

A major factor affecting the readability of a graph drawing is its resolution. In the graph drawing literature, the resolution of a drawing is either measured based on the angles formed by consecutive edges incident to a common node (angular resolution) or by the angles formed at edge crossings (crossing resolution). In this paper, we evaluate both by introducing the notion of "total resolution", that is, the minimum of the angular and crossing resolution. To the best of our knowledge, this is the first time where the problem of maximizing the total resolution of a drawing is studied. The main contribution of the paper consists of drawings of asymptotically optimal total resolution for complete graphs (circular drawings) and for complete bipartite graphs (2-layered drawings). In addition, we present and experimentally evaluate a force-directed based algorithm that constructs drawings of large total resolution.

cs.DS↗

arXiv2010

The Straight-Line RAC Drawing Problem is NP-Hard

Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are greater than 70 degrees. This motivated the study of RAC drawings, in which every pair of crossing edges intersects at right angle. In this work, we demonstrate a class of graphs with unique RAC combinatorial embedding and we employ members of this class in order to show that it is NP-hard to decide whether a graph admits a straight-line RAC drawing.

cs.DS↗

arXiv2009

Crossing-Free Acyclic Hamiltonian Path Completion for Planar st-Digraphs

In this paper we study the problem of existence of a crossing-free acyclic hamiltonian path completion (for short, HP-completion) set for embedded upward planar digraphs. In the context of book embeddings, this question becomes: given an embedded upward planar digraph $G$, determine whether there exists an upward 2-page book embedding of $G$ preserving the given planar embedding. Given an embedded $st$-digraph $G$ which has a crossing-free HP-completion set, we show that there always exists a crossing-free HP-completion set with at most two edges per face of $G$. For an embedded $N$-free upward planar digraph $G$, we show that there always exists a crossing-free acyclic HP-completion set for $G$ which, moreover, can be computed in linear time. For a width-$k$ embedded planar $st$-digraph $G$, we show that we can be efficiently test whether $G$ admits a crossing-free acyclic HP-completion set.

cs.DS↗

arXiv2009

Crossing-Optimal Acyclic HP-Completion for Outerplanar st-Digraphs

Given an embedded planar acyclic digraph G, we define the problem of acyclic hamiltonian path completion with crossing minimization (Acyclic-HPCCM) to be the problem of determining a hamiltonian path completion set of edges such that, when these edges are embedded on G, they create the smallest possible number of edge crossings and turn G to a hamiltonian acyclic digraph. Our results include: 1. We provide a characterization under which a planar st-digraph G is hamiltonian. 2. For an outerplanar st-digraph G, we define the st-polygon decomposition of G and, based on its properties, we develop a linear-time algorithm that solves the Acyclic-HPCCM problem. 3. For the class of planar st-digraphs, we establish an equivalence between the Acyclic-HPCCM problem and the problem of determining an upward 2-page topological book embedding with minimum number of spine crossings. We infer (based on this equivalence) for the class of outerplanar st-digraphs an upward topological 2-page book embedding with minimum number of spine crossings. To the best of our knowledge, it is the first time that edge-crossing minimization is studied in conjunction with the acyclic hamiltonian completion problem and the first time that an optimal algorithm with respect to spine crossing minimization is presented for upward topological book embeddings.

cs.DS↗

arXiv2008

Optimal Acyclic Hamiltonian Path Completion for Outerplanar Triangulated st-Digraphs (with Application to Upward Topological Book Embeddings)

Given an embedded planar acyclic digraph G, we define the problem of "acyclic hamiltonian path completion with crossing minimization (Acyclic-HPCCM)" to be the problem of determining an hamiltonian path completion set of edges such that, when these edges are embedded on G, they create the smallest possible number of edge crossings and turn G to a hamiltonian digraph. Our results include: --We provide a characterization under which a triangulated st-digraph G is hamiltonian. --For an outerplanar triangulated st-digraph G, we define the st-polygon decomposition of G and, based on its properties, we develop a linear-time algorithm that solves the Acyclic-HPCCM problem with at most one crossing per edge of G. --For the class of st-planar digraphs, we establish an equivalence between the Acyclic-HPCCM problem and the problem of determining an upward 2-page topological book embedding with minimum number of spine crossings. We infer (based on this equivalence) for the class of outerplanar triangulated st-digraphs an upward topological 2-page book embedding with minimum number of spine crossings and at most one spine crossing per edge. To the best of our knowledge, it is the first time that edge-crossing minimization is studied in conjunction with the acyclic hamiltonian completion problem and the first time that an optimal algorithm with respect to spine crossing minimization is presented for upward topological book embeddings.

cs.DS↗