14634802
Bounded degree acyclic decompositions of digraphs
An acyclic decomposition of a digraph is a partition of the edges into acyclic subgraphs. Trivially every digraph has an acyclic decomposition into two subgraphs. It is proved that for every integer s ≥ 2 every digraph has an acyclic decomposition into s subgraphs such that in each subgraph the outdegree of each vertex v is at most ⌊deg(v)/s - 1⌋. For all digraphs this degree bound is optimal.
1733138
Grid drawings of k-colourable graphs
It is proved that every k-colourable graph on n vertices has a grid drawing with O(kn) area, and that this bound is best possible. This result can be viewed as a generalisation of the no-three-in-line problem. A further area bound is established that includes the aspect ratio as a parameter.
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.
1804621
The Maximum Number of Edges in a Three-Dimensional Grid-Drawing
An exact formula is given for the maximum number of edges in a graph that admits a three-dimensional grid-drawing contained in a given bounding box. The first universal lower bound on the volume of threedimensional grid-drawings is obtained as a corollary. Our results generalise to the setting of multi-dimensional polyline grid-drawings.
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.
3264071
Layout of Graphs with Bounded Tree-Width
A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queue-number. A three-dimensional (straight-line grid) drawing of a graph represents the vertices by points in $\mathbb{Z}^3$ and the edges by noncrossing line-segments. This paper contributes three main results: 
(1) It is proved that the minimum volume of a certain type of three-dimensional drawing of a graph G is closely related to the queue-number of G. In particular, if G is an n-vertex member of a proper minor-closed family of graphs (such as a planar graph), then G has a $\mathcal{O}(1) \times \mathcal{O}(1) \times \mathcal{O}(n)$ drawing if and only if G has a $\mathcal{O}(1)$ queue-number. 
(2) It is proved that the queue-number is bounded by the tree-width, thus resolving an open problem due to Ganley and Heath [Discrete Appl. Math., 109 (2001), pp. 215--221] and disproving a conjecture of Pemmaraju [Exploring the Powers of Stacks and Queues via Graph Layouts, Ph. D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1992]. This result provides renewed hope for the positive resolution of a number of open problems in the theory of queue layouts. 
(3) It is proved that graphs of bounded tree-width have three-dimensional drawings with $\mathcal{O}(n)$ volume. This is the most general family of graphs known to admit three-dimensional drawings with $\mathcal{O}(n)$ volume. 
The proofs depend upon our results regarding track layouts and tree-partitions of graphs, which may be of independent interest.
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.
31124806
ETOL Forms
5292175
Adaptive cache compression for high-performance processors
Modern processors use two or more levels of cache memories to bridge the rising disparity between processor and memory speeds. Compression can improve cache performance by increasing effective cache capacity and eliminating misses. However, decompressing cache lines also increases cache access latency, potentially degrading performance. In this paper, we develop an adaptive policy that dynamically adapts to the costs and benefits of cache compression. We propose a two-level cache hierarchy where the L1 cache holds uncompressed data and the L2 cache dynamically selects between compressed and uncompressed storage. The L2 cache is 8-way set-associative with LRU replacement, where each set can store up to eight compressed lines but has space for only four uncompressed lines. On each L2 reference, the LRU stack depth and compressed size determine whether compression (could have) eliminated a miss or incurs an unnecessary decompression overhead. Based on this outcome, the adaptive policy updates a single global saturating counter, which predicts whether to allocate lines in compressed or uncompressed form. We evaluate adaptive cache compression using full-system simulation and a range of benchmarks. We show that compression can improve performance for memory-intensive commercial workloads by up to 17%. However, always using compression hurts performance for low-miss-rate benchmarks - due to unnecessary decompression overhead - degrading performance by up to 18%. By dynamically monitoring workload behavior, the adaptive policy achieves comparable benefits from compression, while never degrading performance by more than 0.4%.
9628178
Uniform Interpretations of Grammar Forms
Encouraged by positive experiences with so-called uniform-interpretations of L-forms, we investigate in this paper a suitable analogous definition of uniform interpretations of grammar forms. Concerning CF grammar forms it is shown that a rich variety of language families can be obtained. CF grammar forms with a single variable are extensively examined both with regard to generative capacity (including a characterization of subregular, sublinear and subfinite index families) and with regard to the notion of goodness and badness. Concerning non-CF grammar forms it is shown that each of the families of EOL-, ETOL-, matrix-, scattered context-, context sensitive, type 0-languages (and many others) can be obtained by using interpretations of one form specific to this family.
3174555
A characterization of Thompson digraphs
A finite-state machine is called a Thompson machine if it can be constructed from an empty-free regular expression using the construction of Thompson as modified by Hopcroft and Ullman. We call the underlying digraph of a Thompson machine a Thompson digraph. We characterize Thompson digraphs and we give an algorithm that generates an equivalent regular expression from a Thompson machine that has size linear in the total number of states and transitions. Although the algorithm is simple, it is novel in that the usual constructions of equivalent regular expressions from finite-state machines produce regular expressions that have size exponential in the size of the given machine, in the worst case. The algorithm provides a tentative first step in the construction of small expressions from finite-state machines.