206057505
Algorithmic Graph Embeddings
The complexity of embedding a graph into a variety of topological surfaces is investigated. A new data structure for graph embeddings is introduced and shown to be superior to the previously known data structures. In particular, the new data structure efficiently supports all on-line operations for general graph embeddings. Based on this new data structure, very efficient algorithms are developed to solve the problem “given a graph G and an integer k, construct a genus k embedding for the graph G” for a large range of the integers k and for a large class of 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.
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.
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.
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.
18194069
Avoiding Local Optima in Single Particle Reconstruction
In single-particle reconstruction, a 3D structure is reconstructed from a large number of randomly oriented 2D projections, using techniques related to computed tomography. Unlike in computed tomography, however, the orientations of the projections must be estimated at the same time as the 3D structure, and hence the reconstruction process can be error-prone, converging to an incorrect local optimum rather than the true 3D structure. In this paper, we discuss and further develop a maximum-likelihood approach to reconstruction, and demonstrate that this approach can help avoid incorrect local optima for both 2D and 3D reconstructions.
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.
7679474
Delay Reduction Techniques for Playout Buffering
Receiver synchronization of continuous media streams is required to deal with delay differences and variations resulting from delivery over packet networks such as the Internet. This function is commonly provided using per-stream playout buffers which introduce additional delay in order to produce a playout schedule which meets the synchronization requirements. Packets which arrive after their scheduled playout time are considered late and are discarded. In this paper, we present the Concord algorithm, which provides a delay-sensitive solution for playout buffering. It records historical information and uses it to make short-term predictions about network delay with the aim of not reacting too quickly to short-lived delay variations. This allows an application-controlled tradeoff of packet lateness against buffering delay, suitable for applications which demand low delay but can tolerate or conceal a small amount of late packets. We present a selection of results from an extensive evaluation of Concord using Internet traffic traces. We explore the use of aging techniques to improve the effectiveness of the historical information and hence, the delay predictions. The results show that Concord can produce significant reductions in buffering delay and delay variations at the expense of packet lateness values of less than 1%.
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.
36856498
Defining Soft Sortedness by Abstract Interpretation
Sorted languages can improve the expressiveness and efficiency of reasoning. A conventional sorted language typically includes well-sortedness rules amongst the rules for well-formedness. A major disadvantage of this approach is that many intuitively meaningful expressions are ill-sorted and hence not part of the language.