18478207
Prefix-Free Regular-Expression Matching
We explore the regular-expression matching problem with respect to prefix-freeness of the pattern. We show that the prefix-free regular expression gives only linear number of matching substrings in the size of a given text. Based on this observation, we propose an efficient algorithm for the prefix-free regular-expression matching problem. Furthermore, we suggest an algorithm to determine whether or not a given regular language is prefix-free.
2134196
Counting Structures in Grid Graphs, Cylinders and Tori Using Transfer Matrices: Survey and New Results
There is a very large literature devoted to counting structures, e.g., spanning trees, Hamiltonian cycles, independent sets, acyclic orientations, in the n×m grid graph G(n,m). In particular the problem of counting the number of structures in fixed height graphs, i.e., fixing m and letting n grow, has been, for different types of structures, attacked independently by many different authors, using a transfer matrix approach. This approach essentially permits showing that the number of structures in G(n,m) satisfies a fixed-degree constant-coefficient recurrence relation in n. In contrast there has been surprisingly little work done on counting structures in grid-cylinders (where the left and right, or top and bottom, boundaries of the grid are wrapped around and connected to each other) or in grid-tori (where the left edge of the grid is connected to the right and the top edge is connected to the bottom one). The goal of this paper is to demonstrate that, with some minor modifications, the transfer matrix technique can also be easily used to count structures in fixed height grid-cylinders and tori.
14088697
Approximate shortest paths in anisotropic regions
Our goal is to find an approximate shortest path for a point robot moving in a planar subdivision with <i>n</i> vertices. Let ρ ≥ 1 be a real number. Distances in each face of this subdivision are measured by a convex distance function whose unit disk is contained in a concentric unit Euclidean disk, and contains a concentric Euclidean disk with radius 1/ρ. Different convex distance functions may be used for different faces, and obstacles are allowed. These convex distance functions may be asymmetric. For all ε ∈ (0, 1), and for any two points <i>v<inf>s</inf></i> and <i>v<inf>d</inf></i>, we give an algorithm that finds a path from <i>v<inf>s</inf></i> to <i>v<inf>d</inf></i> whose cost is at most (1 + ε) times the minimum cost. Our algorithm runs in <i>O</i> (ρ<sub>2</sub>logρ/ε<sup>2</sup>n<sup>3</sup> log (ρn/ε)) time. This bound does not depend on any other parameters; in particular, it does not depend on the minimum angle in the subdivision. We give applications to two special cases that have been considered before: the weighted region problem and motion planning in the presence of uniform flows. For the weighted region problem with weights in [1, ρ] ∪ {∞}, the time bound of our algorithm improves to <i>O</i> (ρ<sub>2</sub>logρ/εn<sup>3</sup> log (ρn/ε)).
38202538
Infix-free Regular Expressions and Languages
We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of ...
1333188
Querying approximate shortest paths in anisotropic regions
We present a data structure for answering approximate shortest path queries ina planar subdivision from a fixed source. Let ρ ≥ 1 be a real number.Distances in each face of this subdivision are measured by a possiblyasymmetric convex distance function whose unit disk is contained in aconcentric unit Euclidean disk, and contains a concentric Euclidean disk withradius 1/ρ. Different convex distance functions may be used for differentfaces, and obstacles are allowed. Let ε be any number strictly between 0and 1. Our data structure returns a (1+ε)approximation of the shortest path cost from the fixed source to a querydestination in O(logρn/ε) time. Afterwards, a(1+ε)-approximate shortest path can be reported in time linear in itscomplexity. The data structure uses O(ρ<sup>2</sup> n<sup>4</sup>/ε<sup>2</sup> log ρn/ε) space and can be built in O((ρ<sup>2</sup> n<sup>4</sup>)/(ε<sup>2</sup>)(log ρn/ε)<sup>2</sup>) time. Our time and space bounds do not depend onany geometric parameter of the subdivision such as the minimum angle.
18101194
The Real-Time Process Algebra (RTPA)
The real-time process algebra (RTPA) is a set of new mathematical notations for formally describing system architectures, and static and dynamic behaviors. It is recognized that the specification of software behaviors is a three-dimensional problem known as: (i) mathematical operations, (ii) event/process timing, and (iii) memory manipulations. Conventional formal methods in software engineering were designed to describe the 1-D (type (i)) or 2-D (types (i) and (iii)) static behaviors of software systems via logic, set and type theories. However, they are inadequate to address the 3-D problems in real-time systems. A new notation system that is capable to describe and specify the 3-D real-time behaviors, the real-time process algebra (RTPA), is developed in this paper to meet the fundamental requirements in software engineering.RTPA is designed as a coherent software engineering notation system and a formal engineering method for addressing the 3-D problems in software system specification, refinement, and implementation, particularly for real-time and embedded systems. In this paper, the RTPA meta-processes, algebraic relations, system architectural notations, and a set of fundamental primary and abstract data types are described. On the basis of the RTPA notations, a system specification method and a refinement scheme of RTPA are developed. Then, a case study on a telephone switching system is provided, which demonstrates the expressive power of RTPA on formal specification of both software system architectures and behaviors. RTPA elicits and models 32 algebraic notations, which are the common core of existing formal methods and modern programming languages. The extremely small set of formal notations has been proven sufficient for modeling and specifying real-time systems, their architecture, and static/dynamic behaviors in real-world software engineering environment.
675942
Resource bounded randomness and computational complexity
The following is a survey of resource bounded randomness concepts and their relations to each other. Further, we introduce several new resource bounded randomness concepts corresponding to the classical randomness concepts, and show that the notion of polynomial time bounded Ko randomness is independent of the notions of polynomial time bounded Lutz, Schnorr and Kurtz randomness. Lutz has conjectured that, for a given time or space bound, the corresponding resource bounded Lutz randomness is a proper renement of resource bounded Schnorr randomness. This conjecture is answered for the case of polynomial time bound. Moreover, we will show that polynomial time bounded Schnorr randomness is a proper renement of polynomial time bounded Kurtz randomness. In contrast to this result, we show that the notions of polynomial time bounded Lutz, Schnorr and Kurtz randomness coincide in the case of recursive sets, thus it suces to study the notion of resource bounded Lutz randomness in the context of complexity theory. The stochastic properties of resource bounded random sequences will be discussed in detail. Schnorr has already shown that the law of large numbers holds for p-random sequences. We will show that another important law in probability theory, the law of the iterated logarithm, holds for p-random sequences too. Hence almost all sets in the exponential time complexity class are \hard" from the viewpoint of statistics. c 2000 Elsevier Science B.V. All rights reserved.
2617111
Efficient Algorithms for Traffic Grooming in SONET/WDM Networks
In SONET/WDM optical networks, a wavelength channel is shared by multiple low-rate traffic demands. The multiplexing is known as traffic grooming and carried out by SONET add-drop multiplexers (SADM). A key optimization problem in traffic grooming is to minimize the number of SADMs. This optimization problem is challenging and NP-hard even for unidirectional SONET/WDM rings (UPSR) with symmetric unitary traffic demands. In this paper, we give a linear time heuristic algorithm for this NP-hard problem. Empirical results show that the algorithm outperforms previous algorithms. The algorithm uses the minimum number of wavelengths, which are also precious resources in optical networks. An important subclass of the symmetric unitary traffic pattern is the regular traffic pattern, where each network node appears in exactly r symmetric demands. The regular traffic pattern is a generalization of the well known all-to-all traffic pattern, in which r = n - 1 for a network of n nodes. We prove that the optimization problem remains NP-hard for the regular traffic pattern on the UPSR. We also propose an algorithm for this problem with a better upper bound on the number of used SADMs than previous algorithms. This algorithm always uses the minimum number of wavelengths as well
14047084
Efficient Algorithm for Embedding Hypergraphs in a Cycle
The problem of Minimum Congestion Hypergraph Embedding in a Cycle (MCHEC) is to embed the hyperedges of a hypergraph as paths in a cycle such that the maximum congestion (the maximum number of paths that use any single link in the cycle) is minimized. This problem has many applications, including minimizing communication congestions in computer networks and parallel computations. The MCHEC problem is NP-hard. We give a 1.8-approximation algorithm for the problem. This improves the previous 2-approximation results. The algorithm has the optimal O(mn) time for the hypergraph with m hyperedges and n nodes.
16463784
Privacy Preserving Data Generation for Database Application Performance Testing
Synthetic data plays an important role in software testing. In this paper, we initiate the study of synthetic data generation models for the purpose of application software performance testing. In particular, we will discuss models for protecting privacy in synthetic data generations. Within this model, we investigate the feasibility and techniques for privacy preserving synthetic database generation that can be used for database application performance testing. The methodologies that we will present will be useful for general privacy preserving software performance testing.