34644814
The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers
Let k ≥ 5 be a fixed integer and let m = ⌊(k − 1)/2⌋. It is shown that the independence number of a Ck-free graph is at least c1[∑ d(v)1/(m − 1)](m − 1)/m and that, for odd k, the Ramsey number r(Ck, Kn) is at most c2(nm + 1/log n)1/m, where c1 = c1(m) > 0 and c2 = c2(m) > 0.
1087466
Independence numbers of hypergraphs with sparse neighborhoods
Let H be a hypergraph with N vertices and average degree d. Suppose that the neighborhoods of H are sparse, then its independence number is at least cN(log d/d), where c > 0 is a constant. In particular, let integers r ≥ 3 and n ≥ 1 be fixed, and let H be r-uniform, triangle-free and linear, then its independence number is at least cN logn d/d for all sufficiently large d.
8083367
On Some Three-Color Ramsey Numbers
Abstract. In this paper we study three-color Ramsey numbers. Let Ki,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G1, G2 and G3, if r(G1, G2)≥s(G3), then r(G1, G2, G3)≥(r(G1, G2)−1)(χ(G3)−1)+s(G3), where s(G3) is the chromatic surplus of G3; (ii) (k+m−2)(n−1)+1≤r(K1,k, K1,m, Kn)≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(Kk,m, Kk,m, Kn)≤c(n/logn), and r(C2m, C2m, Kn)≤c(n/logn)m/(m−1) for sufficiently large n.
206570728
On Book-Complete Graph Ramsey Numbers
It is shown that a graph of orderNand average degreedthat does not contain the bookBm=K1+K1, mas a subgraph has independence number at leastNf(d), wheref(x)~(logx/x)(x?∞). From this result we find that the book-complete graph Ramsey number satisfiesr(Bm, Kn)?mn2/log(n/e). It is also shown that for every treeTmwithmedges,r(K1+Tm,Kn)?(2m?1)n2/log(n/e).
2685399
EaseDB: a cache-oblivious in-memory query processor
We propose to demonstrate EaseDB, the first cache-oblivious queryprocessor for in-memory relational query processing. The cache-oblivious notion from the theory community refers to the property that no parameters in an algorithm or a data structure need to be tuned for a specific memory hierarchy for optimality. As a result, EaseDB automatically optimizes the cache performance as well as the overall performance of query processing on any memory hierarchy. We have developed a visualization interface to show the detailed performance of EaseDB in comparison with its cache-conscious counterpart, with both the parameters in the cache-conscious algorithms and the hardware platforms varied.
5296800
Adaptive box-based efficient fault-tolerant routing in 3D torus
In this paper, we propose efficient fault-tolerant routing algorithms for 3D torus with possible large number of faulty nodes. There is no any presumption on the number and the distribution of faulty nodes. The proposed algorithms find a fault-free path between any two nonfaulty nodes with high probability in linear time by using only the local faulty information of the network. The results of our empirical analysis through simulations show that the algorithms can find a fault-free path between any two nonfaulty nodes with a probability higher than 90% in a 3D torus with the number of faulty nodes up to 30%.
16012990
Parallel-array implementations of a non-restoring square root algorithm
In this paper we present a parallel-array implementation of a new non-restoring square root algorithm (PASQRT). The carry-save adder (CSA) is used in the parallel array. The PASQRT has several features unlike other implementations. First, it does not use redundant representation for square root result. Second, each iteration generates an exact resulting value. Next it does not require any conversion on the inputs of the CSA. And last, a precise remainder can be obtained immediately. Furthermore, we present an improved version-a root-select parallel-array implementation (RS-PASQRT) for fast result value generation. The RSPASQRT is capable of achieving up to about 150% speedup ratio over the PASQRT. The simplicity of the implementations indicates that the proposed approach is an alternative to consider when designing a fully pipelined square root unit.
6422073
Efficient Collective Communications in Dual-Cube
The hypercube, or n-cube, has been widely used as the interconnection network in parallel computers. However, the major drawback of the hypercube is the increase in the number of communication links for each node with the increase in the total number of nodes in the system. This paper introduces a new interconnection network, namely dual-cube, for large-scale parallel computers and describes the algorithms for efficient collective communications in dual-cube. The dual-cube network mitigates the problem of increasing number of links in the large-scale hypercube network while retains hypercube's topological properties. Design of efficient routing algorithms for collective communications is the key issue for any interconnection network. In this paper, we show that the collective communications can be done in dual-cube with almost the same communication times as in hypercube.
12730309
Adaptive Neural-Network Control for Redundant Nonholonomic Mobile Modular Manipulators
This paper discusses the trajectory following issue for redundant nonholonomic mobile modular manipulators. Dynamic model is established and an adaptive neural-network controller is developed to control the end-effector to follow a desired spacial trajectory. The proposed algorithm doesn't need any priori dynamics and provides a new solution for stabilization of redundant robotic self-motions. Simulation results for a real robot demonstrate the proposed algorithm is effective.