7031488
Algorithmic aspects of topology control problems for ad hoc networks
Topology control problems are concerned with the assignment of power values to the nodes of an ad hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called textbf monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be bf NP -complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is obtained. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.
40972997
Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks
Topology control problems are concerned with the assignment of power values to the nodes of an ad hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be NP-complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is developed. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.
43626831
Parsing-Driven Generalization for Natural Language Acquisition
Parsing is an important step in natural language processing. It involves tasks of searching for applicable grammatical rules which can transform natural language sentences into their corresponding parse trees. Therefore parsing can be viewed as problem solving, and language acquisition can be achieved by generalizing problem solving heuristics. In this paper we investigate how machine learning methodologies can be integrated with a Wait-And-See Parser (the problem solver) to acquire parsing-related knowledge that is needed for the parser. We call this approach parsing-driven generalization since learning (acquisition of parsing rules and classification of lexicons) is basically derived from the parsing process. Three types of generalization are reported in this paper: simple generalization, generalization by asking questions, and generalization back-propagation. Simple generalization generalizes any two parsing rules whose action parts (right-hand sides) are the same but whose condition parts (left-hand sides) have a single difference. Generalization by asking questions is triggered when a “climbing-up” move on a concept hierarchy is attempted. It is necessary for avoiding over-generalization. Generalization back-propagation propagates a confirmed generalization of some later parsing rule back to its precedent rules in a parsing sequence and thus causes them to be generalized as well. It can reduce the number of questions asked by the system. With these three types of generalization and a mechanism for maintaining lexicon classification (the domain concept hierarchy), parsing and learning can interact to utilize and acquire parsing-related knowledge. To promote the practical performance of parsing after learning, a relaxation parsing mechanism is also designed to process unseen sentences.
28084197
Dynamic category profiling for text filtering and classification
Information is often represented in text form and classified into categories. Unfortunately, automatic classifiers often conduct misclassifications. One of the reasons is that the documents for training the classifiers are mainly from the categories, leading the classifiers to derive category profiles for distinguishing each category from others, rather than measuring the extent to which a document's content overlaps that of a category. To tackle the problem, we present a technique DP4FC that selects suitable features to construct category profiles to distinguish relevant documents from irrelevant documents. More specially, DP4FC is associated with various classifiers. Upon receiving a document, it helps the classifiers to create dynamic category profiles with respect to the document, and accordingly make proper decisions in filtering and classification. Theoretical analysis and empirical results show that DP4FC may significantly promote different classifiers' performances under various environments.
17735073
On problems and conjectures on adjointly equivalent graphs
For a graph G, let h(G,x) denote its adjoint polynomial and @b(G) denote the minimum real root of h(G,x). Two graphs H and G are said to be adjointly equivalent if h(H,x)=h(G,x). Let F"1={G|@b(G)>-4} and F"2={G|@b(G)>=-4}. In this paper, we give a necessary and sufficient condition for two graphs H and G in F"i to be adjointly equivalent, where i=1,2. We also solve some problems and conjectures proposed by Dong et al. (Discrete Math. 258 (2002) 303-321).
18331520
Reliable channel regions for good binary codes transmitted over parallel channels
We study the average error probability performance of binary linear code ensembles when each codeword is divided into J subcodewords with each being transmitted over one of J parallel channels. This model is widely accepted for a number of important practical channels and signaling schemes including block-fading channels, incremental redundancy retransmission schemes, and multicarrier communication techniques for frequency-selective channels. Our focus is on ensembles of good codes whose performance in a single channel model is characterized by a threshold behavior, e.g., turbo and low-density parity-check (LDPC) codes. For a given good code ensemble, we investigate reliable channel regions which ensure reliable communications over parallel channels under maximum-likelihood (ML) decoding. To construct reliable regions, we study a modifed 1961 Gallager bound for parallel channels. By allowing codeword bits to be randomly assigned to each component channel, the average parallel-channel Gallager bound is simplified to be a function of code weight enumerators and channel assignment rates. Special cases of this bound, average union-Bhattacharyya (UB), Shulman-Feder (SF), simplified-sphere (SS), and modified Shulman-Feder (MSF) parallel-channel bounds, allow for describing reliable channel regions using simple functions of channel and code spectrum parameters. Parameters describing the channel are the average parallel-channel Bhattacharyya noise parameter, the average channel mutual information, and parallel Gaussian channel signal-to-noise ratios (SNRs). Code parameters include the union-Bhattacharyya noise threshold and the weight spectrum distance to the random binary code ensemble. Reliable channel regions of repeat-accumulate (RA) codes for parallel binary erasure channels (BECs) and of turbo codes for parallel additive white Gaussian noise (AWGN) channels are numerically computed and compared with simulation results based on iterative decoding. In addition, an examp
37263695
A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs
Let P(G,@l) be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P(H,@l)=P(G,@l) implies [email protected]?G. Koh, Teo and Chia conjectured that for any integers n and k with n>=k+2>=4, the complete tripartite graph K(n-k,n,n) is chromatically unique. Let K(n,m,r)-S denote the graph obtained by deleting all edges in S from the complete tripartite K(n,m,r). In this paper, we establish that for any positive integer n>=m>=r>=2, the chromatic equivalence class of K(n,m,r) is contained in the family {K(x,y,z)-S|1==2k and k>=2.