7767717
On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane
AbstractThe visibility graph V(P) of a point set P \subseteq R2 has vertex set P, such that two points v,w ∈ P are adjacent whenever there is no other point
in P on the line segment between v and w. We study the chromatic number of
V(P). We characterise the 2- and 3-chromatic visibility graphs. It is an open
problem whether the chromatic number of a visibility graph is bounded by its clique
number. Our main result is a super-polynomial lower bound on the chromatic number
(in terms of the clique number).
45354174
On the Parameterized Complexity of Layered Graph Drawing
We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight line-segments between vertices on adjacent layers. We prove that graphs admitting crossing-free h-layer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a linear-time algorithm to decide if a graph has a crossing-free h-layer drawing (for fixed h). This algorithm is extended to solve a large number of related problems, including allowing at most k crossings, or removing at most r edges to leave a crossing-free drawing (for fixed k or r). If the number of crossings or deleted edges is a non-fixed parameter then these problems are NP-complete. For each setting, we can also permit downward drawings of directed graphs and drawings in which edges may span multiple layers, in which case the total span or the maximum span of edges can be minimized. In contrast to the so-called Sugiyama method for layered graph drawing, our algorithms do not assume a preassignment of the vertices to layers.
123081730
Simultaneous diagonal flips in plane triangulations
Simultaneous diagonal flips in plane triangulations are investigated. It is proved that every triangulation with at least six vertices has a simultaneous flip into a 4-connected triangulation, and that it can be computed in linear time. It follows that every triangulation has a simultaneous flip into a Hamiltonian triangulation. This result is used to prove that for any two n-vertex triangulations, there exists a sequence of O(log n) simultaneous flips to transform one into the other. The total number of edges flipped in this sequence is O(n). The maximum size of a simultaneous flip is then studied. It is proved that every triangulation has a simultaneous flip of at least 1/3(n − 2) edges. On the other hand, every simultaneous flip has at most n − 2 edges, and there exist triangulations with a maximum simultaneous flip of 6/7 (n − 2) edges.
122961893
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
32158792
An Algorithm for Three-Dimensional Orthogonal Graph Drawing
In this paper we present an algorithm for 3-dimensional orthogonal graph drawing based on the movement of vertices from an initial layout along the main diagonal of a cube. For an n-vertex m-edge graph with maximum degree six, the algorithm produces drawings with bounding box volume at most 2:37n3 and with a total of 7m/3 bends, using no more than 4 bends per edge route. For maximum degree five graphs the bounding box has volume n3 and each edge route has two bends. These results establish new bounds for 3-dimensional orthogonal graph drawing algorithms and improve on some existing bounds.
341729
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
In this paper we present the first non-trivial lower bounds for the total number of bends in 3-D orthogonal drawings of maximum degree six graphs. In particular, we prove lower bounds for the number of bends in 3-D orthogonal drawings of complete simple graphs and multigraphs, which are tight in most cases. These result are used as the basis for the construction of infinite classes of c-connected simple graphs and multigraphs (2 ≤ c ≤ 6) of maximum degree Δ (3 ≤ Δ ≤ 6) with lower bounds on the total number of bends for all members of the class. We also present lower bounds for the number of bends in general position 3-D orthogonal graph drawings. These results have significant ramifications for the '2-bends' problem, which is one of the most important open problems in the field.
31659897
Scaling the Kowari Metastore
The Kowari Metastore is an Open Source RDF database, built with the goal of providing large-scale storage of Resource Description Framework (RDF) information and a means to analyze that information in near real time. Kowari is currently the most scalable RDF database available. This paper presents a survey of options to further scale the Kowari Metastore. Options to further increase the upper bound of RDF statements which may be stored, decrease write times, distribute computational and storage resource requirements and improve analysis capabilities on large data sets are presented.
12635352
Planar Strong Visibility
Strong visibility is a generalization of standard visibility, defined with respect to a fixed set of line orientations. We investigate computational properties of this generalized visibility, as well as the related notion of strong convexity, and describe algorithms for the following tasks: 1. Testing the strong visibility of two points in a polygon. 2. Finding the strong convex hull of a point set or polygon. 3. Constructing the strong kernel of a polygon. 4. Identifying the points that are strongly visible from a given point.
28831435
On grammar forms with terminal context
SummaryA context-free grammar form G defines a family of context-free grammars {ie397-01}(G). In this paper {ie397-02}(G) is extended to give the family of terminal context grammars {ie397-03}(G), which were introduced by Book [4]. It is shown that the families of languages defined by {ie397-04}(G) and {ie397-05}(G) are equal when G is an ɛ-free context-free grammar form. This generalizes the result of Book [4] for context-free grammars and underlines the usefulness of the notion of grammar forms in formal language theory.
8256982
Memory system behavior of Java-based middleware
In this paper, we present a detailed characterization of the memory system, behavior of ECperf and SPECjbb using both commercial server hardware and Simics full-system simulation. We find that the memory footprint and primary working sets of these workloads are small compared to other commercial workloads (e.g. on-line transaction processing), and that a large fraction of the working sets are shared between processors. We observed two key differences between ECperf and SPECjbb that highlight the importance of isolating the behavior of the middle tier. First, ECperf has a larger instruction footprint, resulting in much higher miss rates for intermediate-size instruction caches. Second, SPECjbb's data set size increases linearly as the benchmark scales up, while ECperf's remains roughly constant. This difference can lead to opposite conclusions on the design of multiprocessor memory systems, such as the utility of moderate sized (i.e. 1 MB) shared caches in a chip multiprocessor.
12582971
Stabbing line segments
An algorithm for the geometric problem of determining a line (called a stabbing line) which intersects each ofn given line segments in the plane is presented. As a matter of fact, the algorithm computes a description of all stabbing lines. A purely geometric fact is proved which infers that this description requiresO(n) space to be specified. Our algorithm computes it inO(n logn) time which is optimal in the worst case.Using the description of the stabbing lines, we are able to decide inO(logn) time whether or not a specified line is a stabbing line. Finally, the problem of maintaining the description of all stabbing lines while inserting and deleting line segments is addressed.