30918175
The Difference Between one Tape and two Tapes: with Respect to Reversal Complexity
Abstract Reversal complexity on 1-tape and 2-tape Turing machine models discussed. We show that with respect to reversal complexity there is an intrinsic difference between 1-tape and 2-tape Turing machines. More precisely, we show that in the deterministic case, 2-tape Turing machines can simulate k-tape Turing machines without much increase in reversals while 1-tape Turing machines do not have such a property if P ≠ PSPACE; in the nondeterministic case, reversal complexity is “too” powerful to be a complexity measure on 2-tape Turing machines, but on 1-tape Turing machines it is a reasonable complexity measure which is linearly related to the space complexity.
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.
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.
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.
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.
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.
41316192
Efficient Learning of Pseudo-Boolean Functions from Limited Training Data
Pseudo-Boolean functions are generalizations of Boolean functions. We present a new method for learning pseudo-Boolean functions from limited training data. The objective of learning is to obtain a function f which is a good approximation of the target function f*. We define suitable criteria for the “goodness” of an approximating function. One criterion is to choose a function f that minimizes the “expected distance” with respect to a distance function d (over pairs of pseudo-Boolean functions) and the uniform distribution over all feasible pseudo-Boolean functions. We define two alternative “distance measures” over pairs of pseudo-Boolean functions, and show that they are are actually equivalent with respect to the criterion of minimal expected distance. We outline efficient algorithms for learning pseudo-Boolean functions according to these criteria. Other reasonable distance measures and “goodness” criteria are also discussed.
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.
9663015
Customizing a geographical routing protocol for wireless sensor networks
Several problems are required to be fixed in order to apply geographical routing protocol greedy perimeter stateless routing (GPSR) in wireless sensor networks. First, GPSR is designed under the assumption of symmetric links (i.e., bidirectional reachability), which is not realistic for many practical sensor networks, since wireless links in sensor networks often are asymmetric. Second, in sensor networks, packet destinations are often marked with locations instead of identifiers like IP address. Therefore, packets are routed to the home node, which is the node geographically closest to the destined location. Under GPSR, when the target location is outside the exterior perimeter of the sensor network, each packet has to visit all nodes on the boundary of the sensor network topology before it identifies the home node, which results in energy inefficiency. Third, due to the dynamic nature of sensor networks, maintaining data consistency, that is, data retrieved from the home node for a location should be consistent with the data sent to the same location, becomes a challenge when home nodes change. We propose on-demand GPSR (OD-GPSR), a data driven geographical routing protocol customized for sensor networks with solutions to the above three problems. Simulation results show that OD-GPSR performs well in terms of energy efficiency and packet delivery rate at the cost of a little bit more packet delivery delay.
7673579
Managing personal and group collections of information
The internet revolution has dramatically increased the amount of information available to users. Various tools such as search engines have been developed to help users find the information they need from this vast repository. Users often also need tools to help manipulate the growing amount of useful information they have discovered. Current tools available for this purpose are typically local components of web browsers designed to manage URL bookmarks. They provide limited functionalities to handle high information complexities.