32850524
Linear inequalities for covering codes: Part I: Pair covering inequalities
The lower bounds on K(n,R), minimum number of codewords of any binary code of length n, and covering radius R are improved. A new technique combining the Hamming association scheme and the results of a classic problem of covering pairs by k-tuples is introduced. The new lower bounds are obtained by studying various linear inequalities satisfied by covering codes, and such an inequality is derived. The lower bounds for K(n,R) are studied for some special values of n and R, which serve as examples showing how the methods developed are applied to concrete cases. >
5201312
Synchronization recovery of variable-length codes
The synchronization recovery property of variable-length (VL) codes has been extensively studied. In the paper, the mean error propagation length (MEPL) and the variance of error propagation length (VEPL), which are the secondary performance criteria of a VL code, are introduced to measure the synchronization recovery capability of a VL code. For the same probability distribution, there exist many different VL codes which have the same redundancy as the Huffman code but quite different MEPLs and VEPLs. To find one of the VL codes which has the minimum MEPL is a very difficult problem. We present two design algorithms for finding minimum-redundancy VL codes with short MEPL and VEPL. These two algorithms are simple and have the property that the codewords are assigned one by one. The efficiency of the algorithms are tested extensively by comparing the algorithms with known construction methods available in literature. Actually, VL codes obtained by the two algorithms outperform almost all codes available.
32960689
On Maximal Shadows of Members in Left-compressed Sets
Whereas Stanley, Proctor and others studied Sperner properties of the poset L(k,m) we consider shadows of left-compressed sets and derive asymptotic bounds on their sizes.
15006226
Bounds on the sizes of constant weight covering codes
Motivated by applications in universal data compression algorithms we study the problem of bounds on the sizes of constant weight covering codes. We are concerned with the minimal sizes of codes of lengthn and constant weightu such that every word of lengthn and weightv is within Hamming distanced from a codeword. In addition to a brief summary of part of the relevant literature, we also give new results on upper and lower bounds to these sizes. We pay particular attention to the asymptotic covering density of these codes. We include tables of the bounds on the sizes of these codes both for small values ofn and for the asymptotic behavior. A comparison with techniques for attaining bounds for packing codes is also given. Some new combinatorial questions are also arising from the techniques.
43476378
Partial converse for a relay channel
A special case of the general discrete memoryless relay channel is studied. This channel consists of an input x, a relay output z, a channel output y, and a noiseless channel of capacity C/sub r/ allowing the relay sender to send additional information to the decoder. The channel is described by a collection of distributions (p(y, z mod x)). The decoder uses the channel output y and a function f(z) of the relay output at a rate no greater than C/sub r/ to recover the message. Some results on the capacity of the channel are obtained. >
19004655
Identification via compressed data
A new coding problem is introduced for a correlated source (X/sup n/,Y/sup n/)/sub n=1//sup /spl infin//. The observer of X/sup n/ can transmit data depending on X/sup n/ at a prescribed rate R. Based on these data the observer of Y/sup n/ tries to identify whether for some distortion measure /spl rho/ (like the Hamming distance) n/sup -1/ /spl rho/(X/sup n/,Y/sup n/)/spl les/d, a prescribed fidelity criterion. We investigate as functions of R and d the exponents of two error probabilities, the probabilities for misacceptance, and the probabilities for misrejection. In the case where X/sup n/ and Y/sup n/ are independent, we completely characterize the achievable region for the rate R and the exponents of two error probabilities; in the case where X/sup n/ and Y/sup n/ are correlated, we get some interesting partial results for the achievable region. During the process, we develop a new method for proving converses, which is called "the inherently typical subset lemma". This new method goes considerably beyond the "entropy characterization" the "image size characterization," and its extensions. It is conceivable that this new method has a strong impact on multiuser information theory.
14083998
Towards CST-enhanced summarization
In this paper, we propose to enhance the process of automatic extractive multi-document text summarization by taking into account cross-document structural relationships as posited in Cross-document Structure Theory (CST). An arbitrary multidocument extract can be CST-enhanced by replacing low-salience sentences with other sentences that increase the total number of CST relationships included in the summary. We show that CST-enhanced summaries outperform their unmodified counterparts using the relative utility evaluation metric. We also show that the effect of a CST relationship on an extract depends on its type.
1951197
A probabilistic semantic model for image annotation and multi-modal image retrieval
This paper addresses automatic image annotation problem and its application to multi-modal image retrieval. The contribution of our work is three-fold. (1) We propose a probabilistic semantic model in which the visual features and the textual words are connected via a hidden layer which constitutes the semantic concepts to be discovered to explicitly exploit the synergy among the modalities. (2) The association of visual features and textual words is determined in a Bayesian framework such that the confidence of the association can be provided. (3) Extensive evaluation on a large-scale, visually and semantically diverse image collection crawled from Web is reported to evaluate the prototype system based on the model. In the proposed probabilistic model, a hidden concept layer which connects the visual feature and the word layer is discovered by fitting a generative model to the training image and annotation words through an Expectation-Maximization (EM) based iterative learning procedure. The evaluation of the prototype system on 17,000 images and 7736 automatically extracted annotation words from crawled Web pages for multi-modal image retrieval has indicated that the proposed semantic model and the developed Bayesian framework are superior to a state-of-the-art peer system in the literature.
24660543
A note on the lower bounds of signed domination number of a graph
Abstract Let G = (V, E) be a graph. For a function f : V → {−1, 1}, the weight of f is w(f) = Σv ∈ V f(v). For a vertex v in V, we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all v ∈ V. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).
38207892
On the Relations Between Arboricity and Independent Number Or Covering Number
In this paper, the following results are obtained: a(G) + β(G) ⩽ p + 1, ⌈p2⌉ ⩽ a(G)β(G), ⌈p2⌉ ⩽ a′(G) + gb′(G) ⩽ pa′(G) + α′(G) ⩽ 2⌈p2⌉ (δ ⩽ 1) and all bounds are sharp, where p = ¦V(G)¦, ⌈x⌉ denotes the smallest integer greater than or equal to x, a(G) is the vertex arboricity, a′(G) is the edge arboricity, α′(G) is the edge covering number, β(G) is the vertex independent number, β′(G) is the edge independent number, and δ is the minimum degree of G.
9335089
Long-term forecasting of Internet backbone traffic: observations and initial models
We introduce a methodology to predict when and where link additions/upgrades have to take place in an IP backbone network. Using SNMP statistics, collected continuously since 1999, we compute aggregate demand between any two adjacent PoPs and look at its evolution at time scales larger than one hour. We show that IP backbone traffic exhibits visible long term trends, strong periodicities, and variability at multiple time scales. Our methodology relies on the wavelet multiresolution analysis and linear time series models. Using wavelet multiresolution analysis, we smooth the collected measurements until we identify the overall long-term trend. The fluctuations around the obtained trend are further analyzed at multiple time scales. We show that the largest amount of variability in the original signal is due to its fluctuations at the 12 hour time scale. We model inter-PoP aggregate demand as a multiple linear regression model, consisting of the two identified components. We show that this model accounts for 98% of the total energy in the original signal, while explaining 90% of its variance. Weekly approximations of those components can be accurately modeled with low-order autoregressive integrated moving average (ARIMA) models. We show that forecasting the long term trend and the fluctuations of the traffic at the 12 hour time scale yields accurate estimates for at least six months in the future.