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.
206964202
Asymptotic Upper Bounds for Ramsey Functions
Abstract. We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nfa+1(d), where fa+1(d)=∫01(((1−t)1/(a+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(Kk+l,Kn)≤ (l+o(1))nk/(logn)k−1. In particular, r(Kk, Kn)≤(1+o(1))nk−1/(log n)k−2.
5363430
Differential Methods for Finding Independent Sets in Hypergraphs
It is shown by using differential methods that if ${\cal H}$ is a double linear, $r$-uniform hypergraph with degree sequence $\{d_v\}$ such that any subhypergraph induced by a neighborhood has maximum degree less than $m$, then its independence number is at least $\sum_{v}f_{r,m}(d_v)$, where $f_{r,m}(x)$ is a convex function satisfying $f_{r,m}(x)\sim (\log x)/x$ if $r=2$ and $c/x^{1/(r-1)}$ if $r \ge 3$, as $x\to\infty$, and $c=c(r,m)>0$ is a constant. The proof yields a polynomial-time algorithm for finding such an independent set in ${\cal H}$.
43234278
A Ramsey Goodness Result for Graphs with Many Pendant Edges
17658871
On generalized Ramsey numbers
Abstract Let f 1 and f 2 be graph parameters. The Ramsey number r ( f 1 ⩾ m ; f 2 ⩾ n ) is defined as the minimum integer N such that any graph G on N vertices, either f 1 ( G )⩾ m or f 2 ( G )⩾n . A general existence condition is given and a general upper bound is shown in this paper. In addition, suppose the number of triangles in G is denoted by t ( G ). We verify that (1−o(1))(24 n ) 1/3 ⩽ r ( t ⩾ n ; t ⩾ n )⩽(1+o(1))(48 n ) 1/3 as n →∞.
34447441
Asymptotic bounds for some bipartite graph: complete graph Ramsey numbers
Abstract The Ramsey number r(H,Kn) is the smallest integer N so that each graph on N vertices that fails to contain H as a subgraph has independence number at least n. It is shown that r(K 2,m ,K n )⩽(m−1+ o (1))(n/ log n) 2 and r(C 2m ,K n )⩽c(n/ log n) m/(m−1) for m fixed and n→∞. Also r(K 2,n ,K n )=Θ(n 3 / log 2 n) and r(C 5 ,K n )⩽cn 3/2 / log n .
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.
17836895
Binomial-Tree Fault Tolerant Routing in Dual-Cubes with Large Number of Faulty Nodes
A dual-cube DC(m) has m + 1 links per node where m is the degree of a cluster (m-cube), and one extra link is used for connection between clusters. The dual-cube mitigates the problem of increasing number of links in the large-scale hypercube network while keeps most of the topological properties of the hypercube network. In this paper, we propose efficient algorithms for finding a nonfaulty routing path between any two nonfaulty nodes in the dual-cube with a large number of faulty nodes. A node v ∈ DC(m) is called k-safe if v has at least k nonfaulty neighbors. The DC(m) is called k-safe if every node in DC(m) is k-safe. The first algorithm presented in this paper is an off-line algorithm that uses global information of faulty status. It finds a nonfaulty path of length at most d(s,t) + O(k2) in O(|F| + m) time for any two nonfaulty nodes s and t in the k-safe DC(m) with number of faulty nodes |F| < 2k(m + 1 – k), where 0≤ k ≤ m/2. The second algorithm is an online algorithm that uses local information only. It can find a fault-free path with high probability in an arbitrarily faulty dual-cube with unbounded number of faulty nodes.
6625111
On incremental and robust subspace learning
Principal Component Analysis (PCA) has been of great interest in computer vision and pattern recognition. In particular, incrementally learning a PCA model, which is computationally efficient for large-scale problems as well as adaptable to reflect the variable state of a dynamic system, is an attractive research topic with numerous applications such as adaptive background modelling and active object recognition. In addition, the conventional PCA, in the sense of least mean squared error minimisation, is susceptible to outlying measurements. To address these two important issues, we present a novel algorithm of incremental PCA, and then extend it to robust PCA. Compared with the previous studies on robust PCA, our algorithm is computationally more efficient. We demonstrate the performance of these algorithms with experimental results on dynamic background modelling and multi-view face modelling.
7190108
NaLIX: an interactive natural language interface for querying XML
Database query languages can be intimidating to the non-expert, leading to the immense recent popularity for keyword based search in spite of its significant limitations. The holy grail has been the development of a natural language query interface. We present NaLIX, a generic interactive natural language query interface to an XML database. Our system can accept an arbitrary English language sentence as query input, which can include aggregation, nesting, and value joins, among other things. This query is translated, potentially after reformulation, into an XQuery expression that can be evaluated against an XML database. The translation is done through mapping grammatical proximity of natural language parsed tokens to proximity of corresponding elements in the result XML. In this demonstration, we show that NaLIX, while far from being able to pass the Turing test, is perfectly usable in practice, and able to handle even quite complex queries in a variety of application domains. In addition, we also demonstrate how carefully designed features in NaLIX facilitate the interactive query process and improve the usability of the interface.
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%.