13571183
Chain Decompositions of 4-Connected Graphs
In this paper we give a decomposition of a $4$-connected graph $G$ into nonseparating chains, which is similar to an ear decomposition of a $2$-connected graph. We also give an $O(|V(G)|^2|E(G)|)$ algorithm that constructs such a decomposition. In applications, the asymptotic performance can often be improved to $O(|V(G)|^3)$. This decomposition will be used to find four independent spanning trees in a $4$-connected graph.
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.
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.
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
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.
2653351
Fingerprint images encryption via multi-scroll chaotic attractors
This paper proposes a chaotic fingerprint images encryption approach. An image of a fingerprint is encrypted via a two-dimensional (2D) chaotic sequence obtained from multi-scroll chaotic attractors. Initial values of the chaotic attractors are served as the private key, which can be generated from the pixel distribution of the binary images of the captured fingerprints. Due to the dynamic uncertainties in the acquisition process of fingerprint images, the keys generated from the pixel value distribution are virtually random. With the elaborately designed 2D chaotic sequence, the encrypted fingerprint images have balanced 0-1 ratio and ideal nonlinearity. Only with the valid private key can the images of fingerprint be recovered. Simulation results and 2D-DFT validate this chaotic encryption approach.
7132341
HASE: A Hybrid Approach to Selectivity Estimation for Conjunctive Predicates
Current methods for selectivity estimation fall into two broad categories, synopsis-based and sampling-based. Synopsis-based methods, such as histograms, incur minimal overhead at query optimization time and thus are widely used in commercial database systems. Sampling-based methods are more suited for ad-hoc queries, but often involve high I/O cost because of random access to the underlying data. Though both methods serve the same purpose of selectivity estimation, their interaction in the case of selectivity estimation for conjuncts of predicates on multiple attributes is largely unexplored. Our work aims at taking the best of both worlds, by making consistent use of synopses and sample information when they are both present. To achieve this goal, we propose HASE, a novel estimation scheme based on a powerful mechanism called generalized raking. We formalize selectivity estimation in the presence of single attribute synopses and sample information as a constrained optimization problem. By solving this problem, we obtain a new set of weights associated with the sampled tuples, which has the nice property of reproducing the known selectivities when applied to individual predicates. We discuss different variants of the optimization problem and provide algorithms for solving it. We also provide asymptotic error bounds on the estimate. Extensive experiments are performed on both synthetic and real data, and the results show that HASE significantly outperforms both synopsis-based and sampling-based methods.
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%.
26301648
Data Integrity Framework and Language Support for Active Web Intermediaries
With the maturity of content adaptation technologies (such as I-CAP and OPES) in web intermediaries and of content personalization in the network, data integrity has already become a key concern when such technologies are deployed. To address this issue, we propose a data integrity framework with the following functionalities: (i) a server can specify its authorizations, (ii) active web intermediaries can provide value-added services in accordance with the server’s intentions, and more importantly, (iii) a client is facilitated to verify the received message with the server’s authorizations and intermediaries’ footprints. With the actual implementation of our data integrity framework in web (content and proxy) servers and clients, we show the feasibility and practicability of our proposed design through its low performance overhead and possible data (re)use.