Papers by Tamara Mchedlidze
Abstract. In this paper, we report on our efforts to identify important Greek web sites on the we... more Abstract. In this paper, we report on our efforts to identify important Greek web sites on the web by analyzing the link structure of Greek web sites. Towards this end, five independent graph-theoretic methods have been deployed: hub and authority, page rank, Bow-Tie structure, core analysis and degree distribution. Our findings indicate that government, non-profit and educational sites are amongst the most important in the Greek web space.
A drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path... more A drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, ie, a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm.
Abstract. A digraph D is unilateral if for every pair x, y of its vertices there exists a directe... more Abstract. A digraph D is unilateral if for every pair x, y of its vertices there exists a directed path from x to y, or a directed path from y to x, or both. A mixed graph M=(V, A, E) with arc-set A and edgeset E accepts a unilateral orientation, if its edges can be oriented so that the resulting digraph is unilateral. In this paper, we present the first linear-time recognition algorithm for unilaterally orientable mixed graphs.
Given a triangulation of a regular n-gon with n≥ 4, a new triangulation can be obtained by flippi... more Given a triangulation of a regular n-gon with n≥ 4, a new triangulation can be obtained by flipping any internal edge. The triangulation resulting from flipping an edge e is obtained by first removing the edge e, and then inserting the diagonal of the resulting quadrilateral that is different from e; see Fig. 1.
Optimal acyclic hamiltonian path completion for outerplanar triangulated st-digraphs (with application to upward topological book embeddings)
Abstract: Given an embedded planar acyclic digraph G, we define the problem of" acyclic hamiltoni... more Abstract: 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:
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-verte... more 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. We also note that our approach can be extended 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.
How many vertex locations can be arbitrarily chosen when drawing planar graphs?
Abstract: It is proven that every set $ S $ of distinct points in the plane with cardinality $\ l... more Abstract: It is proven that every set $ S $ of distinct points in the plane with cardinality $\ lceil\ frac {\ sqrt {\ log_2 n}-1}{4}\ rceil $ can be a subset of the vertices of a crossing-free straight-line drawing of any planar graph with $ n $ vertices. It is also proven that if $ S $ is restricted to be a one-sided convex point set, its cardinality increases to $\ lceil\ sqrt [3]{n}\ rceil $. The proofs are constructive and give rise to O (n)-time drawing algorithms.
Drawing graphs with vertices at specified positions and crossings at large angles
Point-set embeddings and large-angle crossings are two areas of graph drawing that independently ... more Point-set embeddings and large-angle crossings are two areas of graph drawing that independently have received a lot of attention in the past few years. In this paper, we consider problems in the intersection of these two areas. Given the point-set-embedding scenario, we are interested in how much we gain in terms of computational complexity, curve complexity, and generality if we allow large-angle crossings as compared to the planar case.
Computing Research Repository, 2009
In this paper we study the problem of existence of a crossing-free acyclic hamiltonian path compl... more 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.
Computing Research Repository, 2011
We study the problem of Upward Point-Set Embeddability, that is the problem of deciding whether a... more 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 straightline embedding into any convex point set, for any k ≥ 2. Finally we show that the problem of Upward Point-Set Embeddability is NP-complete.
On rho-Constrained Upward Topological Book Embeddings
Giordano, Liotta and Whitesides [1] developed an algorithm that, given an embedded planar st-digr... more Giordano, Liotta and Whitesides [1] developed an algorithm that, given an embedded planar st-digraph and a topological numbering ρ of its vertices, computes in O (n2) time a ρ-constrained upward topological book embedding with at most 2n− 4 spine crossings per edge. The number of spine crossings per edge is asymptotically worst case optimal.
We study the problem of characterizing the directed graphs with an upward straight-line embedding... more We study the problem of characterizing the directed graphs with an upward straight-line embedding into every point set in general or in convex position. We solve two questions posed by Binucci et al. [Computational Geometry: Theory and Applications, 2010]. Namely, we prove that the classes of directed graphs with an upward straight-line embedding into every point set in convex position and with an upward straight-line embedding into every point set in general position do not coincide, and we prove that every directed caterpillar admits an upward straight-line embedding into every point set in convex position. Further, we provide new partial positive results on the problem of constructing upward straight-line embeddings of directed paths into point sets in general position.
Computing Research Repository, 2009
Given an embedded planar acyclic digraph G, we define the problem of acyclic hamiltonian path com... more 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 an acyclic hamiltonian digraph. Our results include:
Computing Upward Topological Book Embeddings of Upward Planar Digraphs
This paper studies the problem of computing an upward topological book embedding of an upward pla... more This paper studies the problem of computing an upward topological book embedding of an upward planar digraph G, ie a topological book embedding of G where all edges are monotonically increasing in the upward direction. Besides having its own inherent interest in the theory of upward book embeddability, the question has applications to well studied research topics of computational geometry and of graph drawing. The main results of the paper are as follows.• Every upward planar digraph G with n vertices admits an upward ...
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Papers by Tamara Mchedlidze