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.
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
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.
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.
16363205
Approximating Longest Cycles in Graphs with Bounded Degrees
Jackson and Wormald conjecture that if $G$ is a 3-connected $n$-vertex graph with maximum degree $d\ge 4$, then $G$ has a cycle of length $\Omega(n^{\log_{d-1}2})$. We show that this conjecture holds when $d-1$ is replaced by $\max\{64,4d+1\}$. Our proof implies a cubic algorithm for finding such a cycle.
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
12758700
Distributed cache updating for the dynamic source routing protocol
On-demand routing protocols use route caches to make routing decisions. Due to mobility, cached routes easily become stale. To address the cache staleness issue, prior work in DSR used heuristics with ad hoc parameters to predict the lifetime of a link or a route. However, heuristics cannot accurately estimate timeouts because topology changes are unpredictable. In this paper, we propose proactively disseminating the broken link information to the nodes that have that link in their caches. We define a new cache structure called a cache table and present a distributed cache update algorithm. Each node maintains in its cache table the information necessary for cache updates. When a link failure is detected, the algorithm notifies all reachable nodes that have cached the link in a distributed manner. The algorithm does not use any ad hoc parameters, thus making route caches fully adaptive to topology changes. We show that the algorithm outperforms DSR with path caches and with Link-MaxLife, an adaptive timeout mechanism for link caches. We conclude that proactive cache updating is key to the adaptation of on-demand routing protocols to mobility.
7732726
Towards a syllabus repository for computer science courses
A syllabus defines the contents of a course, as well as other information such as resources and assignments. In this paper, we report on our work towards creating a syllabus repository of Computer Science courses across universities in the USA. We present some statistics from our initial collection of 8000+ syllabi. We show a syllabus creator that is integrated with Moodle [5] moodle_2006_moodle, an open-source course management system, which allows for the creation of a syllabus for a particular course. Among other information, it includes knowledge units from the Computing Curricula 2001 body of knowledge. The goal of the syllabus repository is to provide added value to the Computer Science Education community, and we present some such offerings. We conclude by presenting our future plans for the syllabus repository. These include using automated techniques to collect and classify syllabi, providing recommendations to instructors when creating a syllabus, and allowing the community to share their syllabi automatically. The syllabus collection will be part of the Computing and Information Technology Interactive Digital Educational Library (CITIDEL), a collection of the National Science Digital Library (NSDL).
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.
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.
13475547
Towards estimating the number of distinct value combinations for a set of attributes
Accurately and efficiently estimating the number of distinct values for some attribute(s) or sets of attributes in a data set is of critical importance to many database operations, such as query optimization and approximation query answering. Previous work has focused on the estimation of the number of distinct values for a single attribute and most existing work adopts a data sampling approach. This paper addresses the equally important issue of estimating the number of distinct value combinations for multiple attributes which we call COLSCARD (for COLumn Set CARDinality). It also takes a different approach that uses existing statistical information (e.g., histograms) available on the individual attributes to assist estimation. We start with cases where exact frequency information on individual attributes is available, and present a pair of lower and upper bounds on COLSCARD that are consistent with the available information, as well as an estimator of COLSCARD based on probability. We then proceed to study the case where only partial information (in the form of histograms) is available on individual attributes, and show how the proposed estimator can be adapted to this case. We consider two types of widely used histograms and show how they can be constructed in order to obtain optimal approximation. An experimental evaluation of the proposed estimation method on synthetic as well as two real data sets is provided.