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.
41440512
Polynomial Time Approximation Schemes and Parameterized Complexity
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.
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.
43055665
Automatic Abstraction of Graphs Based on Node Similarity for Graph Visualization
27213248
Multiresolution recognition of offline handwritten Chinese characters with wavelet transform
The authors propose a novel multiresolution recognition scheme for handwritten Chinese character recognition in which an input pattern is recognized by adopting the coefficients of the wavelet transforms. It is known that wavelet representation provides a coarse-to-fine strategy. The recognition starts from the coarse scale and moves to the finer scales. After preprocessing, the wavelet transform is applied to the kanji image. Then, we make use of the coefficients with the lowest resolution to select 50 candidates from 3755 categories. In order to enhance the statistical feature of a character, we used statistical methods to reconstruct features in fine classification. With the proposed recognition system, experiments are performed on the 863 Testing System. The correct rate reaches 80.56%, which is a promising result.
21231697
Finding and Analyzing Database User Sessions
A database user session is a sequence of queries issued by a user (or an application) to achieve a certain task. Analysis of task-oriented database user sessions provides useful insight into the query behavior of database users. In this paper, we describe novel algorithms for identifying sessions from database traces and for grouping the sessions different classes. We also present experimental results.
16107199
Fast Rectangular Matrix Multiplication and Applications
First we study asymptotically fast algorithms for rectangular matrix multiplication. We begin with new algorithms for multiplication of ann?nmatrix by ann?n2matrix in arithmetic timeO(n?),?=3.333953?, which is less by 0.041 than the previous record 3.375477?. Then we present fast multiplication algorithms for matrix pairs of arbitrary dimensions, estimate the asymptotic running time as a function of the dimensions, and optimize the exponents of the complexity estimates. For a large class of input matrix pairs, we improve the known exponents. Finally we show three applications of our results: (a)we decrease from 2.851 to 2.837 the known exponent of the work bounds for fast deterministic (NC) parallel evaluation of the determinant, the characteristic polynomial, and the inverse of ann?nmatrix, as well as for the solution to a nonsingular linear system ofnequations, (b)we asymptotically accelerate the known sequential algorithms for the univariate polynomial composition modxn, yielding the complexity boundO(n1.667) versus the old record ofO(n1.688), and for the univariate polynomial factorization over a finite field, and (c)we improve slightly the known complexity estimates for computing basic solutions to the linear programming problem withmconstraints andnvariables.
668000
Applying language modeling to session identification from database trace logs
A database session is a sequence of requests presented to the database system by a user or an application to achieve a certain task. Session identification is an important step in discovering useful patterns from database trace logs. The discovered patterns can be used to improve the performance of database systems by prefetching predicted queries, rewriting the current query or conducting effective cache replacement.In this paper, we present an application of a new session identification method based on statistical language modeling to database trace logs. Several problems of the language modeling based method are revealed in the application, which include how to select values for the parameters of the language model, how to evaluate the accuracy of the session identification result and how to learn a language model without well-labeled training data. All of these issues are important in the successful application of the language modeling based method for session identification. We propose solutions to these open issues. In particular, new methods for determining an entropy threshold and the order of the language model are proposed. New performance measures are presented to better evaluate the accuracy of the identified sessions. Furthermore, three types of learning methods, namely, learning from labeled data, learning from semi-labeled data and learning from unlabeled data, are introduced to learn language models from different types of training data. Finally, we report experimental results that show the effectiveness of the language model based method for identifying sessions from the trace logs of an OLTP database application and the TPC-C Benchmark.