29305561
Positively curved cubic plane graphs are finite
Let G be an infinite plane graph such that G is locally finite and every face of G is bounded by a cycle. Then G is said to be positively curved if, for every vertex x of G, 1− d(x)/2 + Σx∈F 1 |F | > 0, where the summation is taken over all facial cycles F containing x. Note that if G is positively curved then the maximum degree of G is at most 5. As a discrete analogue of a result in Riemannian geometry, Higuchi conjectured that if G is positively curved then G is finite. In this paper, we establish this conjecture for cubic graphs. Partially supported by a grant from China Scholarship Council Partially supported by NSF grant DMS-9970527
11130888
On 3-connected graphs with contractible edge covers of size k
Abstract We consider 3-connected graphs whose contractible edges can be covered by k vertices and show that they can be divided into finitely many infinite classes of graphs.
1160338
Graph Connectivity After Path
Removal
Let G be a graph and
u, v be two distinct vertices of
G. A u—v path P is called nonseparating if
G—V(P) is connected. The purpose of this
paper is to study the number of nonseparating
u—v path for two arbitrary
vertices u and
v of a given graph. For a
positive integer k, we will
show that there is a minimum integer α(k) so that if G is an α(k)-connected graph and
u and v are two arbitrary vertices in
G, then there exist
k vertex disjoint paths
P1[u,v], P2[u,v], . . ., Pk[u,v], such that G—V (Pi[u,v]) is connected for every
i (i = 1, 2, ..., k). In fact, we will prove that
α(k) ≤ 22k+2. It is known that α(1) = 3.. A
result of Tutte showed that α(2) = 3. We show that α(3) = 6. In
addition, we prove that if G
is a 5-connected graph, then for every pair of vertices
u and v there exists a path
P[u, v] such that G—V(P[u,
v]) is 2-connected.
21169395
Small Circuit Double Covers of Cubic Multigraphs
Let G be a two-connected graph. A family F of circuits of G is called a circuit double cover (CDC) if each edge of G is contained in exactly two circuits of F. In this paper, we show that if a simple cubic graph G (G ? K4) of order n has a CDC, then G has a CDC containing at most n/2 circuits. This result establishes the equivalence of the circuit double cover conjecture (due to Szekeres, Seymour) and the small circuit double cover conjecture (due to Bondy) for any cubic graph. Actually, a stronger result is obtained in this paper for all loopless cubic graphs. Another result in this paper establishes an upper bound on the size of any CDC of a cubic graph.
8637971
Infinite paths in planar graphs II, structures and ladder nets
A graph is k-indivisible, where k is a positive integer, if the deletion of any finite set of vertices results in at most k − 1 infinite components. In 1971, NashWilliams conjectured that a 4-connected infinite planar graph contains a spanning 2-way infinite path if, and only if, it is 3-indivisible. In this paper, we prove a structural result for 2-indivisible infinite planar graphs. This structural result is then used to prove Nash-Williams conjecture for all 4-connected 2-indivisible infinite planar graphs. ∗Partially supported by NSF grants DMS-9531824 and DMS-9970527
122697425
Infinite paths in planar graphs I: Graphs with radial nets
Let G be an infinite 4-connected planar graph such that the deletion of any finite set of vertices from G results in exactly one infinite component. Dean et al. proved that either G admits a radial net or a special subgraph of G admits a ladder net, and they used these nets to show that G contains a spanning 1-way infinite path. In this paper, we show that if G admits a radial net, then G also contains a spanning 2-way infinite path. This is a step towards a conjecture of Nash-Williams. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 147–162, 2004
1195630
DATIS: A Data Transfer Interface for SPMD Programs of Scientific Computing
10594579
Hard Queries can be Addressed with Query Splitting Plus Stepping Stones and Pathways
A key finding of the Reliable Information Access Workshop of 2003 was that in collections like those used for TREC 6-8, there are a number of hard queries for which no current search engine can return a high quality set of results. Our Stepping Stones and Pathways (SSP) approach may yield an effective solution to such hard problems, as well as support exploration of collections of content not well known to a person (with broad interest and/or complex information needs). Our initial and promising testing of SSP had users prepare two separate short queries in order to launch processing. However, since beginning with a single information need is a more typical initial situation, we have extended the SSP research by exploring query splitting, especially as might apply to handling hard queries. This paper summarizes our recent results and identifies some of the future work needed.
1419192
Trading capacity for performance in a disk array
A variety of performance-enhancing techniques, such as striping, mirroring, and rotational data replication, exist in the disk array literature. Given a fixed budget of disks, one must intelligently choose what combination of these techniques to employ. In this paper, we present a way of designing disk arrays that can flexibly and systematically reduce seek and rotational delay in a balanced manner. We give analytical models that can guide an array designer towards optimal configurations by considering both disk and workload characteristics. We have implemented a prototype disk array that incorporates the configuration models. In the process, we have also developed a robust disk head position prediction mechanism without any hardware support. The resulting prototype demonstrates the effectiveness of the configuration models.
12892754
Reasoning About Approximate Match Query Results
Join techniques deploying approximate match predicates are fundamental data cleaning operations. A variety of predicates have been utilized to quantify approximate match in such operations and some have been embedded in a declarative data cleaning framework. These techniques return pairs of tuples from both relations, tagged with a score, signifying the degree of similarity between the tuples in the pair according to the specific approximate match predicate. In this paper, we consider the problem of estimating various parameters on the output of declarative approximate join algorithms for planning purposes. Such algorithms are highly time consuming, so precise knowledge of the result size as well as its score distribution is a pressing concern. This knowledge aids decisions as to which operations are more promising for identifying highly similar tuples, which is a key operation for data cleaning. We propose solution strategies that fully comply with a declarative framework and analytically reason about the quality of the estimates we obtain as well as the performance of our strategies. We present the results of a detailed performance evaluation of all strategies proposed. Our experimental results validate our analytical expectations and shed additional light on the quality and performance of our estimation framework. Our study offers a set of simple, fully declarative techniques for this problem, which can be readily deployed in data cleaning systems.
16035202
An efficient transistor optimizer for custom circuits
We present an equation-based transistor size optimizer that minimizes delay of custom circuits. Our method uses static timing analysis to find the critical paths and numerical methods to optimize transistor sizes continuously without using simulation. Consequently, it is faster than simulation-based optimizers, and more general than standard cell optimizers. We demonstrate its efficacy and accuracy on a complete dynamic adder presented, where we achieve a 54% speed-up, and final critical path delay that match Spice within 1%.