10668543
Parameterized Computation of LCS for Two Sequences
The problem of finding the longest common subsequence is a well-known optimization problem because of its applications, especially in bioinformatics. In this paper, by applying the techniques developed in parameterized computation, an efficient approach for the problem of finding the longest common subsequence of two sequences is presented. The parameterized approach is compared with the well-known dynamic programming approach for the problem. The parameterized approach is much more efficient, as is shown by the experimental results.
2218327
Strong computational lower bounds via parameterized complexity
We develop new techniques for deriving strong computational lower bounds for a class of well-known NP-hard problems. This class includes weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. For example, although a trivial enumeration can easily test in time O(n^k) if a given graph of n vertices has a clique of size k, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the problem is not solvable in time f(k)n^o^(^k^) for any function f, even if we restrict the parameter values to be bounded by an arbitrarily small function of n. Under the same assumption, we prove that even if we restrict the parameter values k to be of the order @Q(@m(n)) for any reasonable function @m, no algorithm of running time n^o^(^k^) can test if a graph of n vertices has a clique of size k. Similar strong lower bounds on the computational complexity are also derived for other NP-hard problems in the above class. Our techniques can be further extended to derive computational lower bounds on polynomial time approximation schemes for NP-hard optimization problems. For example, we prove that the NP-hard distinguishing substring selection problem, for which a polynomial time approximation scheme has been recently developed, has no polynomial time approximation schemes of running time f(1/@e)n^o^(^1^/^@e^) for any function f unless an unlikely collapse occurs in parameterized complexity theory.
2661456
Linear FPT reductions and computational lower bounds
We develop new techniques for deriving very strong computational lower bounds for a class of well-known NP-hard problems, including weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. For example, although a trivial enumeration can easily test in time O(nk) if a given graph of n vertices has a clique of size k, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the problem is not solvable in time f(k) no(k) for any function f, even if we restrict the parameter value k to be bounded by an arbitrarily small function of n. Under the same assumption, we prove that even if we restrict the parameter values k to be Θ(μ(n)) for any reasonable function μ, no algorithm of running time no(k) can test if a graph of n vertices has a clique of size k. Similar strong lower bounds are also derived for other problems in the above class. Our techniques can be extended to derive computational lower bounds on approximation algorithms for NP-hard optimization problems. For example, we prove that the NP-hard distinguishing substring selection problem, for which a polynomial time approximation scheme has been recently developed, has no polynomial time approximation schemes of running time f(1/ε)no(1/ε) for any function f unless an unlikely collapse occurs in parameterized complexity theory.
15028779
W-Hardness Under Linear FPT-Reductions: Structural Properties and Further Applications
The notion of linear fpt-reductions has been recently used to derive strong computational lower bounds for well-known NP-hard problems. In this paper, we formally investigate the notions of W[t]-hardness and W[t]-completeness under the linear fpt-reduction, and study structural properties of the corresponding complexity classes. Additional complexity lower bounds on important computational problems are also established.
15675165
Maximum Common Subgraph: Upper Bound and Lower Bound Results
In bio informatics, the biological structure matching problems can be formulated as the problem of finding the maximum common subgraph. Among the many different variants of the maximum common subgraph problem, the maximum common induced subgraph of two graphs is of special interest. In this paper, first we derive the lower bound result for the exact algorithms of the maximum common induced subgraph of two graphs, based on the current research progress in the area of parameterized computation. Then we investigate the upper bound and design the approaches for addressing this problem. Basically, this problem can be reduced to find a maximum clique in the product graph of the two given graphs. In consideration of the upper bound result, the obtained lower bound result is asymptotically tight. We would like to point out that our lower bound result presented here is currently best-known
43590220
Lower Bounds and Parameterized Approach for Longest Common Subsequence
In this paper, different parameterized versions of the longest common subsequence (LCS) problem are extensively investigated and computational lower bound results are derived based on current research progress in parameterized computation. For example, with the number of sequences as the parameter k, the problem is unlikely to be solvable in time f(k)no(k), where n is the length of each sequence and f is any recursive function. The lower bound result is asymptotically tight in consideration of the dynamic programming approach of time O(nk). Computational lower bounds for polynomial-time approximation schemes (PTAS) for the LCS problem are also derived. It is shown that the LCS problem has no PTAS of time f(1/ e)no(1/ e) for any recursive function f, unless all SNP problems are solvable in subexponential time. Compared with former results on this problem, this result has its significance. Finally a parameterized approach for the LCS problem is discussed, which is more efficient than the dynamic programming approach, especially when applied to large scale sequences.
11235220
Probability-Based Chinese Text Processing and Retrieval
We discuss the use of probability-based natural language processing for Chinese text retrieval. We focus on comparing different text extraction methods and probabilistic weighting methods. Several docu- ment processing methods and probabilistic weighting functions are presented. A number of experiments have been conducted on large standard text collections. We present the experimental results that com- pare a word-based text processing method with a character-based method. The experimental results also compare a number of term-weighting functions including both single-unit weighting and compound-unit weighting functions. Modern information retrieval (IR) systems should be able to take natural language queries and retrieve documents written in natural languages. One way to process nat- ural language texts in IR is statistical. In this approach, linguistic units are extracted from the documents and queries. Those units extracted from the documents are used to index the documents. Those extracted from a query are weighted according to their degrees of importance. The most important units are chosen as query terms. An infor- mation retrieval system takes the selected query terms, matches the terms with the indexes of documents, calculates a retrieval status value for each matched document using a term-weighting method, and presents the user with potentially relevant docu- ments from a collection of documents. The performance of the information retrieval system in identifying relevant documents greatly depends on the text processing method used. We investigate the effectiveness of different text extraction methods and different term weighting methods in the context of Chinese information retrieval. It is a well- known problem that there is no separator between Chinese words, so Chinese words cannot be used easily to index or search texts as is possible in English. Therefore, some people use characters or n-grams as searchable tokens instead of words. We discuss two text extraction methods. One extraction method uses words, compound words, and phrases in the document and query texts as indexing terms to represent the texts. We refer to this method as the word-based approach. For this approach, text segmentation, which divides both document and query texts into linguistic units, is regarded not only as a necessary precursor but also as a bottleneck of this kind of system (Wu and Tseng 1993). The other extraction method is based on single Chinese characters, in which texts are indexed by the characters appearing in the texts (Chen 1992). By using sin- gle character approaches, a search could be conducted for any multi-character word or phrase identified at search time, no matter whether this word or phrase is in the dic- tionary. Both word-based and character-based methods have been used in information
16574049
Feature Selection with Rough Sets for Web Page Classification
Web page classification is the problem of assigning predefined categories to web pages. A challenge in web page classification is how to deal with the high dimensionality of the feature space. We present a feature reduction method based on the rough set theory and investigate the effectiveness of the rough set feature selection method on web page classification. Our experiments indicate that rough set feature selection can improve the predictive performance when the original feature set for representing web pages is large.
28347745
On global sequence alignment
We present a dynamic programming algorithm for computing a best global alignment of two sequences. The proposed algorithm is robust in identifying any of several global relationships between two sequences. The algorithm delivers a best alignment of two sequences in linear space and quadratic time. We also describe a multiple alignment algorithm based on the pairwise algorithm. Both algorithms have been implemented as portable C programs. Experimental results indicate that for a commonly used set of gap penalties, the new programs produce more satisfactory alignments on sequences of various lengths than some existing pairwise and multiple programs based on the dynamic programming algorithm of Needleman and Wunsch.
945376
Text classification in Asian languages without word segmentation
We present a simple approach for Asian language text classification without word segmentation, based on statistical -gram language modeling. In particular, we examine Chinese and Japanese text classification. With character -gram models, our approach avoids word segmentation. However, unlike traditional ad hoc -gram models, the statistical language modeling based approach has strong information theoretic basis and avoids explicit feature selection procedure which potentially loses significantly amount of useful information. We systematically study the key factors in language modeling and their influence on classification. Experiments on Chinese TREC and Japanese NTCIR topic detection show that the simple approach can achieve better performance compared to traditional approaches while avoiding word segmentation, which demonstrates its superiority in Asian language text classification.
15090488
The Islands Approach to Nearest Neighbor Querying in Spatial Networks
Much research has recently been devoted to the data management foundations of location-based mobile services. In one important scenario, the service users are constrained to a transportation network. As a result, query processing in spatial road networks is of interest. We propose a versatile approach to k nearest neighbor computation in spatial networks, termed the Islands approach. By offering flexible yet simple means of balancing re-computation and pre-computation, this approach is able to manage the trade-off between query and update performance. The result is a single, efficient, and versatile approach to k nearest neighbor computation that obviates the need for using several k nearest neighbor approaches for supporting a single service scenario. The experimental comparison with the existing techniques uses real-world road network data and considers both I/O and CPU performance, for both queries and updates.