31851172
Automata-Driven Efficient Subterm Unification
Syntactic unification has widespread use in computing. There are several operations used in deductive computing such as critical pair generation, paramodulation and narrowing that require unifying a term s with every subterm of another term p. This subterm unification problem can be solved naively by repeatedly unifying s with each subterm of p in isolation. The drawback of doing unification in isolation is that commonality among subterms of p is ignored. We present an algorithm for efficient subterm unification by exploiting this commonality. The central idea used in our algorithm is to reduce the common part computation in unification into a string-matching problem and solve it efficiently using a string-matching automaton. The automaton succinctly captures the commonality between subterms of p. The string-matching approach, in conjunction with two new techniques called bidirectional-reduce and marking enables efficient unification of s with every subterm of p.
5663050
Term Matching on Parallel Computers
Term matching is an important problem that arises very often in term rewriting and in functional and equational programming. We present a new parallel algorithm for the term-matching problem on the EREW (exclusive read, exclusive write) model of parallel computation. Our algorithm assumes a string representation of the two terms as its input. The string representation is first transformed into two labeled ordered trees, and term matching is then performed on these two trees. If n is the length of the input terms, then for any constant ϵ (0 < ϵ ≤ 1) our algorithm uses O(n1-ϵ) processors and takes O(nϵlogn) time. If ϵ = 0, the same algorithm will run in O(log2 n) time. The only other known parallel algorithm for this problem, due to Dwork, Kanellakis, and Stockmeyer, requires O(n2) processors and takes either O(logn) or O(log2n) time. However, their algorithm uses the stronger CREW (concurrent read, exclusive write) model of parallel computation and assumes a DAG (directed acyclic graph) representation of the two terms as its input. On the CRCW (concurrent read, concurrent write) model our algorithm requires n processors and O(log n) time.
42876448
Optimal Speedups for Parallel Pattern Matching in Trees
Tree pattern matching is a fundamental operation that is used in a number of programming tasks such as code optimization in compilers, symbolic computation, automatic theorem proving and term rewriting. An important special case of this operation is linear tree pattern matching in which an instance of any variable in the pattern occurs at most once. If n and m are the number of nodes in the subject and pattern tree respectively and if no restriction is placed on the structure of the trees, then the fastest known sequential algorithm for linear tree pattern matching requires O(nm) time in the worst case.
16348991
Adaptive Pattern Matching
Pattern matching is an important operation used in many applications such as functional programming, rewriting, and rule-based expert systems. By preprocessing the patterns into a DFA-like automaton, we can rapidly select the matching pattern(s) in a single scan of the relevant portions of the input term. This automaton is typically based on left-to-right traversal of the patterns. By adapting the traversal order to suit the set of input patterns, it is possible to considerably reduce the space and matching time requirements of the automaton. The design of such adaptive automata is the focus of this paper. We first formalize the notion of an adaptive traversal. We then present several strategies for synthesizing adaptive traversal orders aimed at reducing space and matching time complexity. In the worst case, however, the space requirements can be exponential in the size of the patterns. We show this by establishing an exponential lower bounds on space that is independent of the traversal order used. We then discuss an orthogonal approach to space minimization based on direct construction of optimal dag automata. Finally, our work brings forth the impact of typing in pattern matching. In particular, we show that several important problems (e.g., lazy pattern matching in ML) are computationally hard in the presence of type disciplines, whereas they can be solved efficiently in the untyped setting.
42187803
Incremental Techniques for Efficient Normalization of Nonlinear Rewrite Systems
In [8] we described a nonlinear pattern-matching algorithm with the best known worst-case and optimal average-case time complexity. In this paper we first report on some experiments conducted on our algorithm. Based on these experiments we believe that our algorithm is useful in speeding up normalization of nonlinear rewrite systems even when it has a small number (≥5) of rewrite rules.
10316561
Variable-depth trie index optimization: theory and experimental results
We develop an efficient approach to Trie index optimization. A Trie is a data structure used to index a file having a set of attributes as record identifiers. In the proposed methodology, a file is horizontally partitioned into subsets of records using a Trie index whose depth of indexing is allowed to vary. The retrieval of a record from the file proceeds by “stepping through” the index to identify a subset of records in the file in which a binary search is performed. This paper develops a taxonomy of optimization problems underlying variable-depth Trie index construction. All these problems are solvable in polynomial time, and their characteristics are studied. Exact algorithms and heuristics for their solution are presented. The algorithms are employed in CRES-an expert system for editing written narrative material, developed for the Department of the Navy. CRES uses several large-to-very-large dictionary files for which Trie indexes are constructed using these algorithms. Computational experience with CRES shows that search and retrieval using variable-depth Trie indexes can be as much as six times faster than pure binary search. The space requirements of the Tries are reasonable. The results show that the variable-depth Tries constructed according to the proposed algorithms are viable and efficient for indexing large-to-very-large files by attributes in practical applications.
560868
An Optimal Algorithm for the Orienteering Tour Problem
Orienteering is a sport in which a competitor selects a path from a start to a destination, visiting control points along the path. Each control point has an associated score, and the travel between control points involves a certain cost. The problem is to select a set of control points to visit, so that the total score is maximized subject to a budget constraint on total cost. Several versions of this problem exist. In the version considered in this research, the start and the destination are the same, and the problem is to construct a subtour of the set of control points. The orienteering problem is a variant of the traveling salesman problem, and arises in vehicle routing and production scheduling situations. This problem has been shown to be NP-hard in the literature. We develop an optimal algorithm to solve this problem, using Lagrangean relaxation within a branch-and-bound framework. The Lagrangean relaxation is solved by a degree-constrained spanning tree procedure. Characteristics of the Lagrangea...
206848861
Blind DC Estimation in the Presence of Non-Gaussian Signal
A method of estimating DC offset based solely on the received signal, without using any training information, is presented. This method takes into account the non-Gaussian statistical distribution of the modulated desired signal in order to produce a DC estimate that is more accurate than the conventional sample average of the received signal. Specifically, two iterative algorithms are derived based on the generalized expectation-maximization algorithms for jointly estimating the DC offset, the noise variance, and the parameters that characterize the signal distribution. As an application, we consider the special case where the modulated signal has a constant-envelope characteristic. Using the GSM/EDGE air interface, we demonstrate that the proposed method yields significant reduction in the DC-offset estimation error, which translates into performance gains in receiver sensitivity when used in direct-conversion receivers.
35337405
A dynamic learning model for on-line quality control using the TAGUCHI approach
Abstract An important philosophy of quality control due to Taguchi rests on the belief that, once quality is designed into the product and the process, very little inspection is necessary. Taguchi evaluates quality in terms of costs incurred, including inspection and adjustment costs apart from quality loss. Using these costs, he determines an optimal interval for periodic inspection of products. At each inspection, the first item on the process line is checked for defects. If no defects are found, the process is assumed to be under control. On the other hand, if the first item turns out to be defective, the process is immediately stopped and adjusted. The underlying assumption here is that, once a defect is observed, it is construed that the process has drifted and all subsequent items are defective. This article challenges the underlying assumption by recognizing that the observation of one defective item does not necessarily imply that the process is out of control. Noisy signals may occur as a result ...
62235624
An efficient approach to stochastic jobshop scheduling: algorithms and empirical investigations
Abstract Jobshop scheduling is one of the important classes of problems planning. The jobshop represents a common manufacturing environment, in which a set of machines is used to process a stream of jobs arriving randomly. The stochastic arrival pattern of the jobs, their processing sequences, and processing times render the scheduling of jobs a complex and difficult task. Furthermore, the scheduling task involves multiple conflicting objectives such as the minimization of the flow time, lateness and the number of late jobs among others. In this research,we develop a framework for the efficient scheduling of jobs considering these multiple objectives. The motivation for this research arises from the good performance of the interactive man-machine scheduling systems in achieving significant levels of attainment in the set of objectives, simultaneously. We develop scheduling strategies to the man-machine approach in this research. The algorithms developed in this research have been extensively tested and evaluated against the traditional scheduling methods using simulation studies. The results show that the proposed approach is efficient and viable for solving practical scheduling problems in the presence of multiple objectives.
32066139
Topographically discounted Internet infrastructure resources: a panel study and econometric analysis
The Internet infrastructure is increasingly utilized for the provision and delivery of a variety of services. The rapid growth and substantial demand fluctuations of the supported services are placing strain on the service providers to effectively manage their infrastructure resources. Capacity Provision Network (CPN) is a market-driven mechanism that enables the service providers to efficiently allocate, share and trade service capabilities. Central to the operation of CPN is the notion of discounted capacities which capture the underlying topology of the Internet. It serves as a practical instrument for service providers to evaluate the utility of capacity services available at remote sites vis-à-vis the capacities available locally and from the content providers. We conducted an Internet based longitudinal field experiment to empirically assess and validate the critical properties of discount factors. Our analysis reveals that discount factors exhibit markedly lower volatility than network delays, and are more stable over seasonal and temporal trend patterns. The results related to size effects suggest that sharing and trade agreements with larger content can be particularly effective. Our finding on the existence of the concavity property points to the ability of intermediation services to enhance the overall gains from resource sharing arrangements.