14221100
Graph Treewidth and Geometric Thickness Parameters
Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph parameter thicknessθ(G). By restricting the edges to be straight, we obtain the geometric thickness${\bar\theta}$(G). By further restricting the vertices to be in convex position, we obtain the book thicknessbt(G). This paper studies the relationship between these parameters and the treewidth of G. Let $\theta({\mathcal T}_{k}) / {\bar\theta}({\mathcal T}_{k}) / {\tt bt}({\mathcal T}_{k})$denote the maximum thickness / geometric thickness / book thickness of a graph with treewidth at most k. We prove that: 
 
– $\theta({\mathcal T}_{k})={\bar\theta}({\mathcal T}_{k}) = \lceil k/2 \rceil$, and 
 
– ${\tt bt}({\mathcal T}_{k}) = k$for k≤2, and ${\tt bt}({\mathcal T}_{k}) = k+1$for k≥3. 
 
The first result says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. The second result disproves the conjecture of Ganley and Heath [Discrete Appl. Math. 2001] that ${\tt bt}({\mathcal T}_{k}) = k$for all k. Analogous results are proved for outerthickness, arboricity, and star-arboricity.
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.
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.
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.
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.
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.
5982937
Improving multiple-CMP systems using token coherence
Improvements in semiconductor technology now enable chip multiprocessors (CMPs). As many future computer systems will use one or more CMPs and support shared memory, such systems will have caches that must be kept coherent. Coherence is a particular challenge for multiple-CMP (M-CMP) systems. One approach is to use a hierarchical protocol that explicitly separates the intra-CMP coherence protocol from the inter-CMP protocol, but couples them hierarchically to maintain coherence. However, hierarchical protocols are complex, leading to subtle, difficult-to-verify race conditions. Furthermore, most previous hierarchical protocols use directories at one or both levels, incurring indirections - and thus extra latency - for sharing misses, which are common in commercial workloads. In contrast, this paper exploits the separation of correctness substrate and performance policy in the recently-proposed token coherence protocol to develop the first M-CMP coherence protocol that is flat for correctness, but hierarchical for performance. Via model checking studies, we show that flat correctness eases verification. Via simulation with micro-benchmarks, we make new protocol variants more robust under contention. Finally, via simulation with commercial workloads on a commercial operating system, we show that new protocol variants can be 10-50% faster than a hierarchical directory protocol.
7022714
Simulating a $2M Commercial Server on a $2K PC
As dependence on database management systems and Web servers increases, so does the need for them to run reliably and efficiently-goals that rigorous simulations can help achieve. Execution-driven simulation models system hardware. These simulations capture actual program behavior and detailed system interactions. The authors have developed a simulation methodology that uses multiple simulations, pays careful attention to the effects of scaling on workload behavior, and extends Virtutech AB's Simics full system functional simulator with detailed timing models. The Wisconsin Commercial Workload Suite contains scaled and tuned benchmarks for multiprocessor servers, enabling full-system simulations to run on the PCs that are routinely available to researchers.
18407931
Dynamic verification of end-to-end multiprocessor invariants
As implementations of shared memory multiprocessors become more complicated, hardware faults will increasingly cause errors that are difficult or impossible to detect with low-level, localized mechanisms. In this paper, we argue for dynamic verification (i.e., on-the-fly checking) of end-to-end, system-wide invariants in shared memory multiprocessors. We develop two invariant checkers based on distributed signature analysis. Our coherence-level checker dynamically verifies that every cache coherence upgrade has a corresponding downgrade elsewhere in the system. Our messagelevel checker verifies that all nodes in an SMP observe the same total order of broadcast requests. We use full-system simulation to show that the checkers detect the targeted errors while not significantly degrading system performance.
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.