44791044
A Generalization of a Theorem of Dirac
In this paper, we give a generalization of a well-known result of Dirac that given any k vertices in a k-connected graph where k?2, there is a circuit containing all of them. We also generalize a result of Haggkvist and Thomassen. Our main result partially answers an open matroid question of Oxley.
17076833
On the Structure of 3-connected Matroids and Graphs
An element e of a 3 -connected matroid M is essential if neither the deletionM\e nor the contraction M/e is 3 -connected. Tutte?s Wheels and Whirls Theorem proves that the only 3 -connected matroids in which every element is essential are the wheels and whirls. In this paper, we consider those 3 -connected matroids that have some non-essential elements, showing that every such matroid M must have at least two such elements. We prove that the essential elements of M can be partitioned into classes where two elements are in the same class if M has a fan, a maximal partial wheel, containing both. We also prove that if an essential element e of M is in more than one fan, then that fan has three or five elements; in the latter case, e is in exactly three fans. Moreover, we show that if M has a fan with 2 k or 2 k+ 1 elements for some k? 2, then M can be obtained by sticking together a (k+ 1)-spoked wheel and a certain 3 -connected minor of M. The results proved here will be used elsewhere to completely determine all 3 -connected matroids with exactly two non-essential elements.
14728640
Public Authentication of 3D Mesh Models
In this paper, a public-key scheme is proposed to authenticate 3D mesh models. It is well known that digital signature schemes can be used for data authentication by generating a separate signature and appending it to the file. Another way is divide the original data into two parts: the content to be authenticated and the cover content. In the embedding process, the signature of the first part is generated and imperceptibly embedded within the cover content to form the signed content. In the authentication process, a new hash value is produced from the signed content and compared with the value decrypted from the retrieved signature for tamper detection. Before we implement such a scheme on polygonal meshes, mesh partitioning technique is used to divide them into patches with a fixed amount of vertices. For each patch, a corresponding signature is generated to replace the least significant bits of vertex coordinates within it so that the tamper can be localized. The experimental results have shown the promising results
38263878
A Longest Cycle Version of Tutte's Wheels Theorem
An edgeeof a minimally 3-connected graphGis non-essential if and only if the graph obtained by contractingefromGis both 3-connected and simple. Suppose thatGis not a wheel. Tutte's Wheels Theorem states thatGhas at least one non-essential edge. We show that each longest cycle ofGcontains at least two non-essential edges. Moreover, each cycle ofGwhose edge set is not contained in a fan contains at least two non-essential edges. We characterize the minimally 3-connected graphs which contain a longest cycle containing exactly two non-essential edges.
61408369
Utility Accrual Real-Time Scheduling under Variable Cost Functions
We present a utility accrual real-time scheduling algorithm called CIC-VCUA for tasks whose execution times are functions of their starting times (and, potentially, other factors). We model such variable execution times using variable cost functions (or VCFs). The algorithm considers application activities that are subject to time/utility function time constraints, execution times described using VCFs, and mutual exclusion constraints on concurrent sharing of non-CPU resources. We consider the twofold scheduling objective of 1) assuring that the maximum interval between any two consecutive, successful completions of job instances in an activity must not exceed the activity period (an application-specific objective) and 2) maximizing the system's total accrued utility while satisfying mutual exclusion resource constraints. Since the scheduling problem is intractable, CIC-VCUA is a polynomial-time heuristic algorithm. The algorithm statically computes worst-case task sojourn times, dynamically selects tasks for execution based on their potential utility density, and completes tasks at specific times. We establish that CIC-VCUA achieves optimal timeliness during underloads, and tightly upper bounds inter and intratask completion times. Our simulation experiments confirm the algorithm's effectiveness and superiority
31035436
Contractible Elements in Graphs and Matroids
Let G be a simple 3-connected graph with at least five vertices. Tutte [13] showed that G has at least one contractible edge. Thomassen [11] gave a simple proof of this fact and showed that contractible edges have many applications. In this paper, we show that there are at most $\frac{|V(G)|}{5}$ vertices that are not incident to contractible edges in a 3-connected graph G. This bound is best-possible. We also show that if a vertex v is not incident to any contractible edge in G, then v has at least four neighbours having degree three, and each such neighbour is incident to exactly two contractible edges. We give short proofs of several results on contractible edges in 3-connected graphs as well. We also study the contractible elements for k-connected matroids. We partially solve an open problem for regular matroids.
10090646
On Multiprocessor Utility Accrual Real-Time Scheduling with Statistical Timing Assurances
We present the first Utility Accrual (or UA) real-time scheduling algorithm for multiprocessors, called gMUA. The algorithm considers an application model where real-time activities are subject to time/utility function time constraints, variable execution time demands, and resource overloads where the total activity utilization demand exceeds the total capacity of all processors. We establish several properties of gMUA including optimal total utility (for a special case), conditions under which individual activity utility lower bounds are satisfied, a lower bound on system-wide total accrued utility, and bounded sensitivity for assurances to variations in execution time demand estimates. Our simulation experiments confirm our analysis and illustrate the algorithm's effectiveness