119496125
Vertex partitions of chordal graphs
A k-tree is a chordal graph with no (k + 2)-clique. An 𝓁-tree-partition of a graph G is a vertex partition of G into 'bags,' such that contracting each bag to a single vertex gives an 𝓁-tree (after deleting loops and replacing parallel edges by a single edge). We prove that for all k ≥ 𝓁 ≥0, every k-tree has an 𝓁-tree-partition in which each bag induces a connected ${\lfloor k} /(\ell+1) \rfloor$-tree. An analogous result is proved for oriented k-trees. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 167172, 2006 
 
Supported by Government of Spain grant MEC SB2003-0270, and by the projects MCYT-FEDER BFM2003-00368 and Gen. Cat 2001SGR00224. Research initiated at the Department of Applied Mathematics and the Institute for Theoretical Computer Science at Charles University, Prague, Czech Republic. Supported by project LN00A056 of the Ministry of Education of the Czech Republic, and by the European Union Research Training Network COMBSTRU (Combinatorial Structure of Intractable Problems).
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.
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.
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.
122961893
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
15716107
Performance Pathologies in Hardware Transactional Memory
Transactional memory is a promising approach to ease parallel programming. Hardware transactional memory system designs reflect choices along three key design dimensions: conflict detection, version management, and conflict resolution. The authors identify a set of performance pathologies that could degrade performance in proposed HTM designs. Improving conflict resolution could eliminate these pathologies so designers can build robust HTM systems.
7533318
Completeness of Context-Free Grammar Forms
The notions of a grammar form and g-interpretation were first introduced in [2]. However, it quickly became apparent, particularly for EOL forms [5], that (strict) interpretations had a wider interest as well as being better motivated mathematically. The study of parsing of grammar forms detailed in [4], the basic investigation in [8] on linear completeness amongst other results, the study of density in [9, lo] and the connections with graph theory shown in [ 1 l] have affirmed this position. The present paper continues the approach of [8] focussing on the characterization of complete grammar forms, that is grammar forms which generate all’ context-free languages. Some decidability problems will also be discussed. For further morivation and background material we refer the reader to [8, 141, while for all unexplained concepts in language theory, see [ 131. After giving the necessary definitions in the remainder of this section we characterize complete grammar forms in Section 2, 3 and 4. In Section 2 we introduce the central concept of expansion spectrum and in Section 3 the recently proved super normal form theorem [ 121, while in Section 4 the characterization is completed and generators and hierarchies are briefly mentioned. Consider context-free grammars G = (V, C, P, S), where Z is the alphabet of terminals, VZ the alphabet of nonterminals, P is the set of productions and
33163861
Finitary and infinitary interpretations of languages
The main result of the paper can be viewed both as a generalization of a classical results concerning colorings of graphs, as well as a very useful over-all theorem from which various specific results concerning grammar and language families can be deduced. Essentially our main result says that, when considering infinitary families obtainable by inverse morphisms, it suffices to consider their finitary parts. Various applications are given, in particular, to grammar forms and context-free languages over infinite alphabets.
45540830
Image tracking in real-time: a transputer emulation of some early mammalian vision processes
By emulating some of the 'early' vision processes believed to occur in the visual cortex of mammals, dramatic savings can be made in the com­ putational efforts usually associated with image processing. This paper describes the design and implementation of a low-cost visual tracking sys­ tem that uses no special signal processing, vector processing nor floating­ point hardware. Its effectiveness relies only on the parallel replication of fast scaler integer processors with low latency communications. The current implementation uses 10 T425 transputers, processes 544 x 544 byte-pixel images at camera frame rates and provides 100 Hz. tracking feedback signals to the camera pan-and-tilt motors with a latency of no more than one-fifth of a second. The system will track any object that occupies the (majority of the) centre of the field of view moving against any background - no special lighting conditio~s or artificial scenery are required. The design and implementation follow naturally parallel struc­ tures and are expressed at all levels in occam.
1943361
Modeling cost/performance of a parallel computer simulator
This article examines the cost/performance of simulating a hypothetical target parallel computer using a commercial host parallel computer. We address the question of whether parallel simulation is simply faster than sequential simulation, or if it is also more cost-effective. To answer this, we develop a performance model of the Wisconsin Wind Tunnel (WWT), a system that simulates cache-coherent shared-memory machines on a message-passing Thinking Machines CM-5. The performance model uses Kruskal and Weiss's fork-join model to account for the effect of event processing time variability on WWT's conservative fixed-window simulation algorithm. A generalization of Thiebaut and Stone's footprint model accurately predicts the effect of cache interference on the CM-5. The model is calibrated using parameters extracted from a fully parallel simulation (p = N), and validated by measuring the speedup as the number of processors (p) ranges from 1 to the number of target nodes (N). Together with simple cost models, the performance model indicates that for target system sizes of 32 nodes and larger, parallel simulation is more cost-effective than sequential simulation. The key intuition behind this result is that large simulations require large memories, which dominate the cost of a uniprocessor; parallel computers allow multiple processors to simultaneously access this large memory.