8790131
Three-Dimensional 1-Bend Graph Drawings
We consider three-dimensional grid-drawings of graphs with at most one bend per edge. Under the additional requirement that the vertices be collinear, we prove that the minimum volume of such a drawing is ( cn), where n is the number of vertices and c is the cutwidth of the graph. We then prove that every graph has a three-dimensional grid-drawing with O(n 3 = log 2 n) volume and one bend per edge. The best previous bound was O(n 3 ).
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.
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.
122961893
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
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.
6984741
Bandwidth adaptive snooping
This paper advocates that cache coherence protocols use a bandwidth adaptive approach to adjust to varied system configurations (e.g., number of processors) and workload behaviors. We propose Bandwidth Adaptive Snooping Hybrid (BASH), a hybrid protocol that ranges from behaving like snooping (by broadcasting requests) when excess bandwidth is available to behaving like a directory protocol (by unicasting requests) when bandwidth is limited. BASH adapts dynamically by probabilistically deciding to broadcast or unicast on a per request basis using a local estimate of recent interconnection network utilization. Simulations of a microbenchmark and commercial and scientific workloads show that BASH robustly performs as well or better than the best of snooping and directory protocols as available bandwidth is varied. By mixing broadcasts and unicasts, BASH outperforms both snooping and directory protocols in the mid-range where a static choice of either is inefficient.
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.
29004467
Coherent Network Interfaces for Fine-Grain Communication
1926264
L Codes and Number Systems
Abstract The notion of an L code is introduced as a generalization of the customary notion of a code. Attention is focused on unary L codes. where the target alphabet consists of one letter only. Unary L codes can be identified with such number systems where the representation is unique. Surprisingly many unary morphisms are L codes. Furthermore, even for non-L-codes there is only one ‘exceptional length’ We also give a complete classification for the binary case.
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.