29710029
Covering convex sets with non-overlapping polygons
Abstract We prove that given n ⩾3 convex, compact, and pairwise disjoint sets in the plane, they may be covered with n non-overlapping convex polygons with a total of not more than 6 n −9 sides, and with not more than 3 n −6 distinct slopes. Furthermore, we construct sets that require 6 n −9 sides and 3 n −6 slopes for n ⩾3. The upper bound on the number of slopes implies a new bound on a recently studied transversal problem.
34776029
Embedding between 2-D meshes of the same size
It is shown how to embed an x/sub 1/ /spl times/ 1/sub 1/ mesh M/sub 1/ into an s/sub 2/ /spl times/ t/sub 2/ mesh M/sub 2/, where s/sub 1/ /spl times/ t/sub 2/, s/sub 1/ < t/sub i/ (i = 1,2) such that the dilation is minimized. It is assumed that load = 1 and expansion = 1. For each case there is shown a lower bound on the dilation and a corresponding embedding method. The dilations by these embedding algorithms either match a lower bound or are very close to a lower bound.<<ETX>>
44324303
Equivalent permutation capabilities between time division optical omega network and non-optical extra stage omega network
Since optical networks must support crosstalk-free (CF) connections, regular N/spl times/N multistage interconnection networks (MINs) cannot be directly used to provide connections between N inputs and N outputs. A solution is to use a 2N/spl times/2N Cube-Type MIN to provide the N/spl times/N connections. C. Qiao (1993) proposed a time domain approach that divides the N optical inputs into several groups such that CF connections can be provided by an N/spl times/N regular MIN in several time slots, one for each group. The set of N-permutations realizable in two slots is defined as class /spl theta/. Qiao proved that the size of /spl theta/ is larger than the size of class /spl Omega/, where /spl Omega/ consists of all N-permutations passible through a regular N/spl times/N Omega network. The paper first presents an optimal O(NlgN) time algorithm for identifying whether a given permutation belongs to class /spl theta/ or not. From this algorithm, the paper proves an interesting fact that the class /spl theta/ is identical to the class /spl Omega/+1 which represents the set of N-permutations admissible by a non-optical N/spl times/N one-extra stage Omega network.
9442074
Generalized Latin squares II
Abstract This paper is a continuation of a study on a new class of combinatorial structures called generalized Latin squares or 〈k,l〉-Latin squares. Here, we study the existence question of perfect 〈k,l〉-Latin squares. The main result is an existence theorem for the case M = 2, where M is the multiplicity of the generalized Latin squares. Specifically, we show that for given positive integers N, k = ip, l = iq, where i = gcd(k,l), there exists a perfect 〈k,l〉-Latin square of order N with M = 2 if and only if (i) N = 4k, (ii) pq(p + q)| N, and (iii) q|2.
37059740
Realization of an Arbitrary Permutation on a Hypercube
We present an explicit combinatorial algorithm for constructing a 2-realization for any given permutation on a circuit-switched d-dimensional hypercube (d-cube) such that the total number of directed edges used in the realization (counting every repetition) is bounded by d2d, the total number of directed edges in the d-cube. As a corollary, this result implies a (2d−3) step realization on a packet-switched d-cube (d⩾3).
33412339
Conservative Algorithms for Parallel and Sequential Integer Sorting
We present a conservative CRCW parallel algorithm for integer sorting. This algorithm sorts n integers from {0, 1, ..., m−1} in time O(n log log min(m,n)/p + log n) using p processors. The simulation of our parallel algorithm on the sequential machine yields a sequential algorithm for integer sorting which sorts n integers from {0, 1, ..., m−1} in time O(n min(log log n, log log m/log n)).
6579321
Discovering interesting patterns through user's interactive feedback
In this paper, we study the problem of discovering interesting patterns through user's interactive feedback. We assume a set of candidate patterns (ie, frequent patterns) has already been mined. Our goal is to help a particular user effectively discover interesting patterns according to his specific interest. Without requiring a user to explicitly construct a prior knowledge to measure the interestingness of patterns, we learn the user's prior knowledge from his interactive feedback. We propose two models to represent a user's prior: the log linear model and biased belief model. The former is designed for item-set patterns, whereas the latter is also applicable to sequential and structural patterns. To learn these models, we present a two-stage approach, progressive shrinking and clustering, to select sample patterns for feedback. The experimental results on real and synthetic data sets demonstrate the effectiveness of our approach.
10424667
Miss Rate Prediction Across Program Inputs and Cache Configurations
Improving cache performance requires understanding cache behavior. However, measuring cache performance for one or two data input sets provides little insight into how cache behavior varies across all data input sets and all cache configurations. This paper uses locality analysis to generate a parameterized model of program cache behavior. Given a cache size and associativity, this model predicts the miss rate for arbitrary data input set sizes. This model also identifies critical data input sizes where cache behavior exhibits marked changes. Experiments show this technique is within 2 percent of the hit rate for set associative caches on a set of floating-point and integer programs using array and pointer-based data structures. Building on the new model, this paper presents an interactive visualization tool that uses a three-dimensional plot to show miss rate changes across program data sizes and cache sizes and its use in evaluating compiler transformations. Other uses of this visualization tool include assisting machine and benchmark-set design. The tool can be accessed on the Web at http://www.cs.rochester.edu/research/locality
302118
A Hierarchical Model of Reference Affinity
To improve performance, data reorganization needs locality models to identify groups of data that have reference affinity. Much past work is based on access frequency and does not consider accessing time directly. In this paper, we propose a new model of reference affinity. This model considers the distance between data accesses in addition to the frequency. Affinity groups defined by this model are consistent and have a hierarchical structure. The former property ensures the profitability of data packing, while the latter supports data packing for storage units of different sizes. We then present a statistical clustering method that identifies affinity groups among structure fields and data arrays by analyzing training runs of a program. When used by structure splitting and array regrouping, the new method improves the performance of two test programs by up to 31%. The new data layout is significantly better than that produced by the programmer or by static compiler analysis.
9894542
Reliability optimization of distributed access networks with constrained total cost
In this paper, we study the system reliability optimization of distributed access networks subject to a constraint on the total cost. We first formulate the cost-constrained system reliability optimization problem as a searching process in a combinatorial tree, which enumerates all the possible solutions to the problem. Because the calculation of each possible solution for the reliability problem is extremely time-consuming, a novel algorithm, the Shrinking & Searching Algorithm (SSA), is proposed to speed up the searching process. SSA jointly considers the upper bound of the system reliability for each branch in the combinatorial tree, and the cost constraint on the possible solutions. It avoids most of the redundant calculations in the searching process by gradually shrinking the difference between lower & upper bounds of the length of a path in the corresponding combinatorial tree, which represents a feasible solution. Case study & simulation results are presented to demonstrate the performance of the SSA.
768133
Performance analysis of TCP-friendly AIMD algorithms for multimedia applications
In this paper, the performance of TCP-friendly generic AIMD (Additive Increase and Multiplicative Decrease) algorithms for Web-based playback and multirate multimedia applications is investigated. The necessary and sufficient TCP-friendly condition is derived, and the effectiveness and responsiveness of AIMD are studied. Due to practical implications, a Dynamic TCP-friendly AIMD (DTAIMD) algorithm is proposed. Extensive simulation results are given to verify the derived necessary and sufficient condition, and to demonstrate the performance of the proposed DTAIMD algorithm.