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
16450923
The circumference of a graph with no K3, t-minor
It was shown by Chen and Yu that every 3-connected planar graph G contains a cycle of length at least |G|^l^o^g^"^3^2, where |G| denotes the number of vertices of G. Thomas made a conjecture in a more general setting: there exists a function @b(t)>0 for t>=3, such that every 3-connected graph G with no K"3","t-minor, t>=3, contains a cycle of length at least |G|^@b^(^t^). We prove that this conjecture is true with @b(t)=log"8"t"^"t"^"+"^"12. We also show that every 2-connected graph with no K"2","t-minor, t>=3, contains a cycle of length at least |G|/t^t^-^1.
18288842
Finding Four Independent Trees
Motivated by a multitree approach to the design of reliable communication protocols, Itai and Rodeh gave a linear time algorithm for finding two independent spanning trees in a 2-connected graph. Cheriyan and Maheshwari gave an $O(|V|^2)$ algorithm for finding three independent spanning trees in a 3-connected graph. In this paper we present an $O(|V|^3)$ algorithm for finding four independent spanning trees in a 4-connected graph. We make use of chain decompositions of 4-connected graphs.
11486473
Circumference of Graphs with Bounded Degree
Karger, Motwani, and Ramkumar Algorithmica, 18 (1997), pp. 82--98] have shown that there is no constant approximation algorithm to find a longest cycle in a Hamiltonian graph, and they conjectured that this is the case even for graphs with bounded degree. On the other hand, Feder, Motwani, and Subi [SIAM J. Comput., 31 (2002), pp. 1596--1607] have shown that there is a polynomial time algorithm for finding a cycle of length $n^{\log_32}$ in a 3-connected cubic n-vertex graph. In this paper, we show that if G is a 3-connected n-vertex graph with maximum degree at most d, then one can find, in O(n3) time, a cycle in G of length at least $\Omega(n^{\log_b2})$, where $b=2(d-1)^2+1$.
8099466
Nonseparating Planar Chains in 4-Connected Graphs
In this paper, we describe an O(|V(G)||E(G)|) algorithm for finding a nonseparating planar chain in a 4-connected graph G, which will be used to decompose an arbitrary 4-connected graph into planar chains. This work was motivated by the study of a multitree approach to reliability in distributed networks, as well as the study of nonseparating induced paths in highly connected 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
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.
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.
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.
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%.