19987062
On the construction of most reliable networks
The construction of most reliable networks is investigated. In particular, the study of restricted edge connectivity shows that general Harary graphs are max λ-min mi for all i=λ, λ+1,....2λ- 3. As a consequence, this implies that for each pair of positive integers n and e, there is a graph of n vertices and e edges that is max λ-min mi for all i= λ,λ + 1,....2λ - 3. General Harary graphs that are max λ-min mi for all i= λ, λ + 1,.... 2λ - 2 are also constructed.
5242879
Interactive rind modeling
In this paper, we describe a technique, with roots in topological graph theory, that we call rind modeling. It provides for the easy creation of surfaces resembling peeled and punctured rinds. We show how the method's two main steps of: 1) creation of a shell or crust like the rind of an orange, and 2) opening holes in the crust by punching or peeling can be encapsulated into a real time semi-automatic interactive algorithm. We include a number of worked examples, some by students in a first modeling course, that demonstrate the ease with which a large variety of intricate rind shapes can be created.
16331940
Optimal Parallel Routing in Star Networks
Star networks have recently been proposed as attractive alternatives to the popular hypercube for interconnecting processors on a parallel computer. In this paper, we present an efficient algorithm that constructs an optimal parallel routing in star networks. Our result improves previous results for the problem.
2261180
Graph Ear Decompositions and Graph Embeddings
Ear decomposition of a graph has been extensively studied in relation to graph connectivity. In this paper, a connection of ear decomposition to graph embeddings is exhibited. It is shown that constructing a maximum-paired ear decomposition of a graph and constructing a maximum-genus embedding of the graph are polynomial-time equivalent. Applications of this connection are discussed.
1021255
A minimal and complete set of operators for the development of robust manifold mesh modelers
In this paper, we identify a minimal and complete set of fundamental operators, which is necessary and sufficient for performing all homeomorphic and topological operations on 2- manifold mesh structures. Efficient algorithms are developed for the implementation of these operators. We also developed a set of powerful, user-friendly, and effective operators at the level of user-interface. Using these operators, we have developed a prototype system for robust, interactive, and user-friendly modeling of orientable 2-manifold meshes. Users of our system can perform a large set of homeomorphic and topological changes with these user-interface level operators. Our system is topologically robust in the sense that users will never create invalid 2-manifold mesh structure with these operators. In our system, the homeomorphic and topological surgery operations can be applied alternatively on 2-manifold meshes. With our system, users can blend surfaces, construct rinds, and open holes on these rind shapes. With our system, the shapes that look like solid, non-manifold, or 2-manifold with boundary can be manipulated. The system also provides automatic texture mapping during topology changes.
31382426
Strong Fault-Tolerance: Parallel Routing in Networks with Faults
A d-regular network G is strongly fault-tolerant if for any copy Gf of G with at most d - 2 faulty nodes, every pair of nonfaulty nodes u and v in Gf admits min{df(u), df (v)} node-disjoint paths in Gf from u to v, where df(u) and df(v) are the degrees of the nodes u and v in Gf. We show that popular network structures, such as hypercube and star networks, are strongly fault-tolerant. We develop efficient algorithms that construct the maximum number of node-disjoint paths of optimal or nearly optimal length in these networks with faulty nodes. Our algorithms are optimal in terms of their running time.
20277412
Adaptive hypertext navigation based on user goals and context
Hypertext systems allow flexible access to topics of information, but this flexibility has disadvantages. Users often become lost or overwhelmed by choices. An adaptive hypertext system can overcome these disadvantages by recommending information to users based on their specific information needs and preferences. Simple associative matrices provide an effective way of capturing these user preferences. Because the matrices are easily updated, they support the kind of dynamic learning required in an adaptive system.HYPERFLEX, a prototype of an adaptive hypertext system that learns, is described. Informal studies with HYPERFLEX clarify the circumstances under which adaptive systems are likely to be useful, and suggest that HYPERFLEX can reduce time spent searching for information by up to 40%. Moreover, these benefits can be obtained with relatively little effort on the part of hypertext authors or users.The simple models underlying HYPERFLEX's performance may offer a general and useful alternative to more sophisticated modelling techniques. Conditions under which these models, and similar adaptation techniques, might be most useful are discussed.
8954904
Modification of the AdaBoost-based Detector for Partially Occluded Faces
While face detection seems a solved problem under general conditions, most state-of-the-art systems degrade rapidly when faces are partially occluded by other objects. This paper presents a solution to detect partially occluded faces by reasonably modifying the AdaBoost-based face detector. Our basic idea is that the weak classifiers in the AdaBoost-based face detector, each corresponding to a Haar-like feature, are inherently a patch-based model. Therefore, one can divide the whole face region into multiple patches, and map those weak classifiers to the patches. The weak classifiers belonging to each patch are re-formed to be a new classifier to determine if it is a valid face patch - without occlusion. Finally, we combine all of the valid face patches by assigning the patches with different weights to make the final decision whether the input subwindow is a face. The experimental results show that the proposed method is promising for the detection of occluded faces
33412733
Learning a Hidden Graph Using O(log n) Queries Per Edge
We consider the problem of learning a general graph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden graph. This model has been studied for particular classes of graphs by Kucherov and Grebinski [1] and Alon et al.[2], motivated by problems arising in genome sequencing. We give an adaptive deterministic algorithm that learns a general graph with n vertices and m edges using O(m log n) queries, which is tight up to a constant factor for classes of non-dense graphs. Allowing randomness, we give a 5-round Las Vegas algorithm using \(O(m {\rm log}n+\sqrt{m}{\rm log}^{2}n)\) queries in expectation. We give a lower bound of Ω((2m/r) r/2) for learning the class of non-uniform hypergraphs of dimension r with m edges. For the class of r-uniform hypergraphs with bounded degree d, where d≤ n 1/( r− − 1)/(2r 1 + 2/( r− − 1)), we give a non-adaptive Monte Carlo algorithm using O(dnlog n) queries, which succeeds with probability at least 1–n − − c, where c is any constant.
27409853
The Strong Semantics for Logic Programs
Recently, the well-founded semantics of a logic program P has been strengthened to the well-founded semantics-by-case (WF C ) and then again to the extended well-founded semantics (WF E ). An important concept used in both WF C and WF E is that of derived rules. We extend the notion of derived rules by adding a new type of derivation and define the strong semantics of P, which has the following important property, known as the GCWA-property: if an atom p = false in all minimal models of P, then p = false in the strong semantics of P. In general, the WF C -semantics and the WF E -semantics do not have the GCWA-property. If we first apply the WF E -semantics to P and then apply the strong semantics to a suitably simplified form of P based on its WF E -semantics, then the resulting semantics is stronger than the WF E -semantics and has the GCWA-property.
36905463
Quasi-threshold Graphs
Abstract Quasi-threshold graphs are defined recursively by the following rules: 1. (1) K1 is a quasi-threshold graph, 2. (2) adding a new vertex adjacent to all vertices of a quasi-threshold graph results in a quasi-threshold graph, 3. (3) the disjoint union of two quasi-threshold graphs is a quasi-threshold graph. This paper gives some new equivalent definitions of a quasi-threshold graph. From them, linear time recognition algorithms follow. We also give linear time algorithms for the edge domination problem and the bandwidth problem in this class of graphs.