17726002
Average-case completeness of a word problem for groups
This paper presents a bounded word problem for groups whose random instances are hard on average. The problem is to decide, when given a finitely presented group G, words ~, y, z, and an integer k, whether (Z–lyZ)Z can be obtained from Z(x–l yz) in G using elementary Tietze transformations for at most k times. We show that the problem is average-case NP-complete when instances are chosen at random under a uniform distribution. NP-completeness of more general bounded word problems for groups is shown as well.
17604851
Efficient point coverage in wireless sensor networks
We study minimum-cost sensor placement on a bounded 3D sensing field, R, which comprises a number of discrete points that may or may not be grid points. Suppose we have ℓ types of sensors available with different sensing ranges and different costs. We want to find, given an integer σ ≥ 1, a selection of sensors and a subset of points to place these sensors such that every point in R is covered by at least σ sensors and the total cost of the sensors is minimum. This problem is known to be NP-hard. Let ki denote the maximum number of points that can be covered by a sensor of the ith type. We present in this paper a polynomial-time approximation algorithm for this problem with a proven approximation ratio $${\gamma = \sum_{i=1}^{\ell} k_{i} -\sigma+1}$$. In applications where the distance of any two points has a fixed positive lower bound, each ki is a constant, and so we have a polynomial-time approximation algorithms with a constant guarantee. While γ may be large, we note that it is only a worst-case upper bound. In practice the actual approximation ratio is small, even on randomly generated points that do not have a fixed positive minimum distance between them. We provide a number of numerical results for comparing approximation solutions and optimal solutions, and show that the actual approximation ratios in these examples are all less than 3, even though γ is substantially larger.
40322050
Complete on Average Boolean Satisfiability
Abstract We present in this paper a dynamic binary coding scheme α on CNF formulas ψ , and show that under a uniform distribution μ α on binary string α ( ψ ), SAT is complete on average, where μ α ( ψ ) is proportional to ∣ α ( ψ )∣ −2 2 −∣ α ( ψ )∣ . We then show that there is k 0 >2 such that for all k ⩾ k 0 , k SAT under μ α is complete on average.
32837558
On average P vs. average NP
Structures of polynomial-time computable distributions and polynomial-time many-one reductions on randomized decision problems are investigated. The scope is widened from the most studied class DNP (distributional-NP) to the class ANP (average-NP), which consists of randomized decision problems accepted by nondeterministic Turing machines in average polynomial time. Results indicate that the structures of average-case complexity classes are very different from their counterparts in worst-case complexity due to the complex structures of probability distributions and distribution functions.<<ETX>>
205093793
On p-Creative Sets and p-Completely Creative Sets
Abstract We study p-creative sets and p-completely creative sets. We first prove that for recursively enumerable sets, p-creativeness is equivalent to p-complete creativeness and Myhill's theorem still holds in the polynomial setting. We then consider p-creativity and p-complete creativity for time complexity classes. We prove that for P, p-creativeness is equivalent to p-complete creativeness. Moreover, we prove that a set A is p-m-complete for DEXT iff A is p-creative for P in DEXT. Since every p-m-complete set for DEXT is p-1-complete (Berman, 1977), we know that Myhill's theorem still holds for P in DEXT. These results can also be proved for NP in NEXT. k -creative sets and k -completely creative sets in NP are next studied. ( k,l )-creative sets and ( k,l )-completely creative sets in a more general setting are defined and shown to exist. It is known that k -completely creative sets are NP-complete (Joseph and Young, 1985), but it is not known whether the converse is true. We approach this problem based on our “double diagonalization” technique of showing that every p-m-complete set for DEXT is p-creative for P. A new class of k -completely creative sets is constructed as well.
206565969
Immunity of Complete Problems
Abstract Two necessary and sufficient conditions for all E -complete sets to contain dense P subsets are shown. We then prove that every ≤ p m -hard for E set and its complement contain dense E ∩UP subsets. As a corollary, every NE -complete set and its complement contain dense E ∩UP subsets.
21513395
VLSI architecture and implementation for FS1016 CELP decoder with reduced power and memory requirements
Abstract The code-excited linear predictive (CELP) coder is the most effective technique among various linear predictive coding methods for speech compression. Hence, designing a relatively low-cost and low-power CELP decoder chip for the portable systems and wireless digital communication environment becomes increasingly important. This paper presents the VLSI architecture and chip implementation for the FS1016 CELP decoder with reduced power and memory requirements. A single-chip implementation of the CELP decoder drastically reduces the cost and the size of many CELP vocoder systems. The decoder chip can achieve the following: (1) excellent accuracy results due to the accuracy studies for the finite word length, (2) power savings and high-speed operations owing to the combined advantages of pipeline and concurrent processing structures, (3) table size reducing by applying the memoryless realization for stochastic codebook and partial sums technique and (4) specification satisfying the FS1016 CELP coder. Fabricated with 0.8 μm double-metal CMOS technology, the chip contains approximately 13 000 transistors occupying a 6.1 × 6.2 mm2 area. It has been tested to be fully functional at IMS XL-60 tester and is the first working FS1016 CELP 4.8 K decoder chip. In particular, the fixed-point accuracy studies for the CELP decoder are also addressed herein.
21909317
Generating Concept Hierarchies from Text for Intelligence Analysis
It is important to automatically extract key information from sensitive text documents for intelligence analysis. Text documents are usually unstructured and information extraction from texts usually focuses on named entity extraction that is insufficient to reflect the concepts contained within documents. Other research on texts focuses on classifying the whole text into categories. However, texts might be diverse in subjects and suffer from classification accuracy. In this paper, our goal is to present a feasible approach to extract relevant information from texts and organize into concept hierarchies with the help of Web corpora. The approach is designed considering the need of information intelligence and the adaptation to different application domains.
9854659
Query Processing for Distance Metrics
In applications such as vision and molecular biology, a common problem is to find the similar objects to a given target (according to some distance measure) in a large database. This paper presents a scheme for query processing in such situations. The basic strategy is to (partially) precompute inter-object distances, and by using the distance information and the triangle inequality, we eliminate the need to calculate certain object distances while evaluating queries. We propose several heuristics that may speed up query evaluation. A series of experiments are then performed to evaluate the effectiveness of our scheme and the relative performance of the heuristics for different queries. Finally we investigate the possibility of parallelizing our scheme through simulation. Our results show that parallelism is best applied in the later stages in evaluating a query.
891661
Fast prefix matching of bounded strings
Longest Prefix Matching (LPM) is the problem of finding which string from a given set is the longest prefix of another, given string. LPM is a core problem in many applications, including IP routing, network data clustering, and telephone network management. These applications typically require very fast matching of bounded strings, i.e., strings that are short and based on small alphabets. We note a simple correspondence between bounded strings and natural numbers that maps prefixes to nested intervals so that computing the longest prefix matching a string is equivalent to finding the shortest interval containing its corresponding integer value. We then present retries, a fast and compact data structure for LPM on general alphabets. Performance results show that retries often outperform previously published data structures for IP look-up. By extending LPM to general alphabets, retries admit new applications that could not exploit prior LPM solutions designed for IP look-ups.
1365809
New techniques for extracting features from protein sequences
In this paper we propose new techniques to extract features from protein sequences. We then use the features as inputs for a Bayesian neural network (BNN) and apply the BNN to classifying protein sequences obtained from the PIR (Protein Information Resource) database maintained at the National Biomedical Research Foundation. To evaluate the performance of the proposed approach, we compare it with other protein classifiers built based on sequence alignment and machine learning methods. Experimental results show the high precision of the proposed classifier and the complementarity of the bioinformatics tools studied in the paper.