1993570
Contractible Cliques in k-Connected Graphs
Kawarabayashi proved that for any integer k≥4, every k-connected graph contains two triangles sharing an edge, or admits a k-contractible edge, or admits a k-contractible triangle. This implies Thomassen's result that every triangle-free k-connected graph contains a k-contractible edge. In this paper, we extend Kawarabayashi's technique and prove a more general result concerning k-contractible cliques.
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.
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
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.
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
1493351
Circuit Design Style for Energy Efficiency: LSDL and Compound Domino
Introduction of sub-90nm technology has made a profound impact on circuit designs. Thus, it requires understanding of existing design styles for desired energy-efficiency. We compare adder designs in the energy-delay space, implemented with Limited Switch Dynamic Logic (LSDL) and Compound Domino Logic (CD) in a 65nm SOI technology. Evaluation results show that LSDL can provide more than 35% energy savings than CD with 25% switching activity at relaxed cycle times greater than 10.5 F04.
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%.
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.
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.
8993397
A Novel Hybrid Crypto-Biometric Authentication Scheme for ATM Based Banking Applications
This paper studies the smartcard based fingerprint encrytion/auth-entication scheme for ATM banking systems. In this scheme, the system authenticates each user by both his/her possession (smartcard) and biometrics (fingerprint). A smartcard is used for the first layer of authentication. Based on the successful pass of the first layer authentication, a subsequent process of the biometric fingerprint authentication proceeds. The proposed scheme is fast and secure. Computer simulations and statistical analyze are presented.