12493274
A Linear-Time Algorithm for Isomorphism of Graphs of Bounded Average Genus
A structure theorem is proved for the class of graphs of bounded average genus, which leads to a linear-time algorithm for isomorphism of such graphs.
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.
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.
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.
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.
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.
27797614
Interacting with Visible Human data using an ImmersaDesk
Interaction with medical volume data has often been difficult, due to the large memory and computational power required. By taking advantage of current high-end graphics hardware, we have developed a volumetric virtual environment that provides the ability to help people interact with the volumetric Visible Human data set. The application enables the user to explore the interior of a virtual human body in a natural and intuitive way.
14053079
Face Samples Re-lighting for Detection Based on the Harmonic Images
Different environment illumination has a great impact on face detection. In this paper, we present a solution by the face relighting based on the harmonic images. The basic idea is that there exist nine harmonic images which can be derived from a 3D model of a face, and by which we can estimate the illumination coefficient of any face samples. To detect faces under the certain lighting conditions, we relight those original face samples to get more new face samples under the various possible lighting conditions by an illumination ratio image and then add them to the training set. By train a classifier based on Support Vector Machine (SVM), the experimental results turn out that the relighting subspace is effective during the detection under the diverse lighting conditions. We also use the relighting database to train an AdaBoost-based face detector and test it on the MIT+CMU frontal face test set. The experimental results show that the data collection can be efficiently speeded up by the proposed methods.
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.
6192242
Computing Maximum-Scoring Segments in Almost Linear Time
Given a sequence, the problem studied in this paper is to find a set of k disjoint continuous subsequences such that the total sum of all elements in the set is maximized. This problem arises naturally in the analysis of DNA sequences. The previous best known algorithm requires Θ(n log n) time in the worst case. For a given sequence of length n, we present an almost linear-time algorithm for this problem. Our algorithm uses a disjoint-set data structure and requires O(nα(n, n)) time in the worst case, where α(n, n) is the inverse Ackermann function.
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.