2381269
Track Layouts of Graphs
Graph drawing problems originate from diverse application domains. In some, such as software engineering and cartography, graphs are required to be visualized or drawn in ways that are easy to read and understand. In others, such as VLSI design, graphs are required to be laid out while satisfying some physical constraint. For example, when a drawing is to be displayed on a page or a computer screen, or is to be used for VLSI design, it is important to keep its area/volume small to avoid wasting space. 
More often than not however, the idea of a good drawing, regardless of its purpose, coincides with having no edge crossings or having very few crossings. Unfortunately, whichever of the numerous drawing styles one considers, a problem requiring a crossing minimization of sorts will, almost certainly, be NP -hard. The theory of fixed parameter tractability (FPT) provides a new and promising approach for coping with intractable problems. In the first part of this thesis we apply algorithmic techniques developed in this theory to well-known graph drawing problems. In particular, we contribute efficient FPT algorithms for crossing minimization and planarization problems concerning the 2-layer drawing style. 
In the second part of this thesis we introduce and comprehensively study so-called track layouts of graphs and their subdivisions. A relationship between this combinatorial structure and several well-known types of graph layouts is established, leading to a number of new results. For example, our study of track layouts of bounded treewidth graphs settles an open problem due to Ganley and Heath (2001) regarding queue layouts of such graphs. Moreover, the study also establishes that graphs of bounded treewidth have three-dimensional straight-line grid drawings with linear volume. 
Through the study of track layouts of subdivisions, we determine that every graph with n vertices and m edges has a three-dimensional polyline grid drawing with the vertices on a rectangular prism, O (n + m log n) volume and O (log n) bends per edge.
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.
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.
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
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.
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
5731433
Specifying and Verifying a Broadcast and a Multicast Snooping Cache Coherence Protocol
We develop a specification methodology that documents and specifies a cache coherence protocol in eight tables: the states, events, actions, and transitions of the cache and memory controllers. We then use this methodology to specify a detailed, modern three-state broadcast snooping protocol with an unordered data network and an ordered address network that allows arbitrary skew. We also present a detailed specification of a new protocol called multicast snooping (Bilir et al., 1999) and, in doing so, we better illustrate the utility of the table-based specification methodology. Finally, we demonstrate a technique for verification of the multicast snooping protocol, through the sketch of a manual proof that the specification satisfies a sequentially consistent memory model.
14349700
Normal form algorithms for extended context-free grammars
We investigate the complexity of a variety of normal-form transformations for extended context-free grammars, where by extended we mean that the set of right-hand sides for each nonterminal in such a grammar is a regular set. The study is motivated by the implementation project GraMa which will provide a C++ toolkit for the symbolic manipulation of context-free objects just as Grail does for regular objects. Our results generalize known complexity bounds for context-free grammars but do so in nontrivial ways. Specifically, we introduce a new representation scheme for extended context-free grammars (the symbol-threaded expression forest), a new normal form for these grammars (dot normal form) and new regular expression algorithms. Copyright 2001 Elsevier Science B.V.
28004475
EOL forms
SummaryIn this paper the notions of “L form” and its “interpretations” are introduced to define families of structurally similar L systems. The families of L systems thus defined are studied from a number of different points of view. It is felt that this novel approach will shed new light on many questions concerning L systems.