9108460
Reversal Complexity
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.
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.
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.
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.
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.
10227949
Analysis of nonsmooth vector-valued functions associated with second-order cones
Abstract.Let be the Lorentz/second-order cone in . For any function f from to , one can define a corresponding function fsoc(x) on by applying f to the spectral values of the spectral decomposition of x∈ with respect to . We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as (ρ-order) semismoothness. These results are useful for designing and analyzing smoothing methods and nonsmooth methods for solving second-order cone programs and complementarity problems.
18278456
On General Results for All-to-All Broadcast
All-to-all broadcast refers to the process by which every node broadcasts its certain piece of information to all other nodes in the system. In this paper, we develop all-to-all broadcast schemes by dealing with two classes of schemes. A prior scheme based on generation of minimal complete sets is first described, and then a new scheme based on propagation of experts is developed. The former always completes the broadcasting in the minimal number of steps and the latter is designed to minimize the number of messages. Performance of these two classes of schemes is comparatively analyzed. The all-to-all broadcast scheme desired can be derived by combining the advantages of these two classes of schemes.
14652586
A simple typed intermediate language for object-oriented languages
Traditional class and object encodings are difficult to use in practical type-preserving compilers because of the complexity of the encodings. We propose a simple typed intermediate language for compiling object-oriented languages and prove its soundness. The key ideas are to preserve lightweight notions of classes and objects instead of compiling them away and to separate name-based subclassing from structure-based subtyping. The language can express standard implementation techniques for both dynamic dispatch and runtime type tests. It has decidable type checking even with subtyping between quantified types with different bounds. Because of its simplicity, the language is a more suitable starting point for a practical type-preserving compiler than traditional encoding techniques.
11661855
Theoretical Analysis of XL over Small Fields
XL was first introduced to solve determined or overdetermined systems of equations over a finite field as an “algebraic attack” against multivariate cryptosystems. There has been a steady stream of announcements of cryptanalysis of primitives by such attacks, including stream ciphers (e.g. Toyocrypt), PKC’s, and more controversially block ciphers (AES/Rijndael and Serpent).
43754145
Heaps with Bits
In this paper, we show how to improve the complexity of heap operations and heapsort using extra bits. We first study parallel complexity of implementing priority queue operations on a heap. While the insertion of a new element into a heap can be done as fast as parallel searching, we show how to delete the smallest element from a heap in constant time with a sublinear number of processors, and in sublogarithmic time with a sublogarithmic number of processors. The models of parallel computation used are the CREW PRAM and the CRCW PRAM. Our results improve those of previously known algorithms.