Augmented infinitesimal perturbation analysis: An alternate explanation

Augmented infinitesimal perturbation analysis (APA) was introduced by Gaivoronski [1991] to increase the purview of the theory of Infinitesimal Perturbation Analysis (IPA). In reference [Gaivoronski 1991] it is shown that an unbiased estimate for the gradient of a class of performance measures of DEDS represented bygeneralized semi-Markov processes (GSMPs) (cf. [Glynn 1989] can be expressed as a sum of an IPA-estimate and a term that takes into account the event order changes. In this paper we present an alternate approach to establishing the result of Gaivoronski, and from this we derive a necessary and sufficient condition for the validity of the IPA algorithm for this class of performance measures. Finally we validate our results by simulation examples.This research was supported by the National Science Foundation under grant number ECS-85-15449, Office of Naval Research Grants Nos. N00014-90-K-1093 and N00014-89-J-1023 and by Army Grant No. DAAL-03-86-K-0171.     

Optimizing discrete event dynamic systems via the gradient surface method

In this paper we propose a gradient surface method (GSM) for the optimization of discrete event dynamic systems. GSM combines the advantages of response surface methodology (RSM) and efficient derivative estimation techniques like perturbation analysis (PA) or likelihood ratio method (LR). In GSM, the gradient estimation is obtained by PA (or LR), and the performance gradient surface is obtained from observations at various points in a fashion similar to the RSM. Zero points of the successive approximating gradient surface are then taken as the estimates of the optimal solution. GSM is characterized by several attractive features: it is a single-run method and more efficient than RSM; it uses at each iteration step the information from all data points rather than just the local gradient; it tries to capture the global features of the gradient surface and thereby quickly arrives at the vicinity of the optimal solution. A number of examples are exhibited to illustrate this method.This work was supported by the Office of Naval Research Grants Nos. N00014-90-K-1093 and N00014-89-J-1023, by National Science Foundation Grant No. ECS-85-15449 and by Army Grant No. DAAL-03-86-K-0171.     

Action transducers and timed automata

Thetimed automaton model of [LyV92, LyV93] is a general model for timing-based systems. A notion oftimed action transducer is here defined as an automata-theoretic way of representing operations on timed automata. It is shown that two timed trace inclusion relations are substitutive with respect to operations that can be described by timed action transducers. Examples are given of operations that can be described in this way, and a preliminary proposal is given for an appropriate language of operators for describing timing-based systems.A preliminary version of this paper appeared in W.R. Cleaveland, editor,Proceedings CONCUR'92, Stony Brook, New York. LNCS 630, pages 436–455. Springer, 1992.Supported by ONR contracts N00014-85-K-0168 and N00014-91-J-1988, by NSF grant CCR-8915206, and by ARPA contracts N00014-89-J-1988 and N00014-92-J-4033.Supported by ESPRIT BRA 7166 CONCUR2 and by the HCM network EXPRESS. Part of the work on this paper was done while the author was at the Ecole des Mines, CMA, Sophia Antipolis, France, and at CWI, Amsterdam, The Netherlands.     

Fast algorithms for bit-serial routing on a hypercube

In this paper we describe anO(logN)-bit-step randomized algorithm for bit-serial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of on-line circuit switching in anO(1)-dilated hypercube (i.e., the problem of establishing edge-disjoint paths between the nodes of the dilated hypercube for any one-to-one mapping).Our algorithm is adaptive and we show that this is necessary to achieve the logarithmic speedup. We generalize the Borodin-Hopcroft lower bound on oblivious routing by proving that any randomized oblivious algorithm on a polylogarithmic degree network requires at least (log² N/log logN) bit steps with high probability for almost all permutations.This research was supported by the Defense Advanced Research Projects Agency under Contracts N00014-87-K-825 and N00014-89-J-1988, the Air Force under Contract AFOSR-89-0271, and the Army under Contract DAAL-03-86-K-0171. This work was completed while the third and fourth authors were at the Laboratory for Computer Science, Massachusetts Institute of Technology.     

Strong consistency of infinitesimal perturbation analysis for tandem queueing networks

Strong consistency of infinitesimal perturbation analysis for the sojourn times in a class of tandem queueing networks is proved. Service times at the queues are correlated, and they are affine functions of the variable parameters. Differentiability of the average sojourn times is not assumed, but proved. The analysis is not based on assumptions of regenerative cycles of the networks but on stability and ergodicity of the queueing processes involved. The proof of strong consistency is based on a set of abstract conditions, described in terms of properties of the sample performance functions. These conditions are first shown to be sufficient for strong consistency, and then their validity for the networks in question is proved.Research supported in part by the NSF under grants Nos. ECS85-15449 and CDR-8803012, under ONR contract nos. N00014-90-K-1093 and N00014-89-J-1023, and under Army contract no. DAAL-03-83-K-0171. This author is now with the Department of Manufacturing Engineering, Boston University, Boston, MA 02215.     

A 2n−2 step algorithm for routing in ann ×n array with constant-size queues

In this paper we describe a deterministic algorithm for solving any 1–1 packet-routing problem on ann ×n mesh in 2n–2 steps using constant-size queues. The time bound is optimal in the worst case. The best previous deterministic algorithm for this problem required time 2n+(n/q) using queues of size (q) for any 1qn, and the best previous randomized algorithm required time 2n+(logn) using constant-size queues.This research was supported by the Clear Center at UTD, DARPA Contracts N00014-91-J-1698 and N00014-92-J-1799, Air Force Contract F49620-92-J-0125, Army Contract DAAL-03-86-K-0171, an NSF Presidential Young Investigator Award with matching funds from AT&T and IBM, and by the Texas Advanced Research Program under Grant No. 3972. A preliminary version of this paper appeared in [5].     

A comparison of simulation techniques and algebraic techniques for verifying concurrent systems

Simulation-based assertional techniques and process algebraic techniques are two of the major methods that have been proposed for the verification of concurrent and distributed systems. It is shown how each of these techniques can be applied to the task of verifying systems described as input/output automata; both safety and liveness properties are considered. A small but typical circuit is verified in both of these ways, first using forward simulations, an execution correspondence lemma, and a simple fairness argument, and second using deductions within the process algebra DIOA for I/O automata. An extended evaluation and comparison of the two methods is given.Supported by NSF grant CCR-89-15206, by DARPA contracts N00014-89-J-1988 and N00014-92J-4033, and by ONR contract N00014-91-J-1046.     

A modular drinking philosophers algorithm

Summary A variant of the drinking philosophers algorithm of Chandy and Misra is described and proved correct in a modular way. The algorithm of Chandy and Misra is based on a particular dining philosophers algorithm and relies on certain properties of its implementation. The drinking philosophers algorithm presented in this paper is able to use an arbitrary dining philosophers algorithm as a subroutine; nothing about the implementation needs to be known, only that it solves the dining philosophers problem. An important advantage of this modularity is that by substituting a more time-efficient dining philosophers algorithm than the one used by Chandy and Misra, a drinking philosophers algorithm withO(1) worst-case waiting time is obtained, whereas the drinking philosophers algorithm of Chandy and Misra hasO(n) worst-case waiting time (forn philosophers). Careful definitions are given to distinguish the drinking and dining philosophers problems and to specify varying degrees of concurrency. Jennifer L. Welch received her B.A. in 1979 from the University of Texas at Austin, and her S.M. and Ph.D. from the Massachusetts Institute of Technology in 1984 and 1988 respectively. She has been a member of technical staff at GTE Laboratories Incorporated in Waltham, Massachusetts and an assistant professor at the University of North Carolina at Chapel Hill. She is currently an assistant professor at Texas A&M University. Her research interests include algorithms and lower bounds for distributed computing.Much of this work was performed while this author was at the Laboratory for Computer Science, Massachusetts Institute of Technology, supported by the Advanced Research Projects Agency of the Department of Defense under contract N00014-83-K-0125, the National Science Foundation under grants DCR-83-02391 and CCR-86-11442, the Office of Army Research under contract DAAG29-84-K-0058, and the Office of Naval Research under contract N00014-85-K-0168. This author was also supported in part by NSF grant CCR-9010730, an IBM Faculty Development Award, and NSF Presidential Young Investigator Award CCR-9158478This author was supported by the Office of Naval Research under contract N00014-91-J-1046, the Advanced Research Projects Agency of the Department of Defense under contract N00014-89-J-1988, and the National Science Foundation under grant CCR-89-15206. The photograph and autobiography of Professor N.A. Lynch were published in Volume 6, No. 2, 1992 on page 121     

Planar geometric location problems

We present anO(n ² log³ n) algorithm for the two-center problem, in which we are given a setS ofn points in the plane and wish to find two closed disks whose union containsS so that the larger of the two radii is as small as possible. We also give anO(n ² log⁵ n) algorithm for solving the two-line-center problem, where we want to find two strips that coverS whose maximum width is as small as possible. The best previous solutions of both problems requireO(n ³) time.Pankaj Agarwal has been supported by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), an NSF Science and Technology Center, under Grant STC-88-09648. Micha Sharir has been supported by the Office of Naval Research under Grants N00014-89-J-3042 and N00014-90-J-1284, by the National Science Foundation under Grant CCR-89-01484, by DIMACS, and by grants from the US-Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development. A preliminary version of this paper has appeared inProceedings of the Second Annual ACM-SIAM Symposium on Discrete Algorithms, 1991, pp. 449–458.     

On generalized signal-to-noise ratios in quadratic detection

The generalized signal-to-noise ratio (GSNR) is a measure of performance often used in evaluating binary hypothesis testing procedures. In this paper, we investigate the properties of the GSNR as applied to the evaluation of quadratic detectors with Gaussian hypotheses. Appealing to reproducing kernel Hilbert space theory, we give a representation for the GSNR that is particularly useful for evaluating extremal properties. Finally, we discuss an alternative performance measure that is both intuitively appealing and superior to the GSNR in some respects.This research was supported by the U.S. Office of Naval Research under Grant N00014-89-J-1321.     

Ray shooting in polygons using geodesic triangulations

LetP be a simple polygon withn vertices. We present a simple decomposition scheme that partitions the interior ofP intoO(n) so-called geodesic triangles, so that any line segment interior toP crosses at most 2 logn of these triangles. This decomposition can be used to preprocessP in a very simple manner, so that any ray-shooting query can be answered in timeO(logn). The data structure requiresO(n) storage andO(n logn) preprocessing time. By using more sophisticated techniques, we can reduce the preprocessing time toO(n). We also extend our general technique to the case of ray shooting amidstk polygonal obstacles with a total ofn edges, so that a query can be answered inO( logn) time.Work by Bernard Chazelle has been supported by NSF Grant CCR-87-00917. Work by Herbert Edelsbrunner has been supported by NSF Grant CCR-89-21421. Work by Micha Sharir has been supported by ONR Grants N00014-89-J-3042 and N00014-90-J-1284, by NSF Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.     

Timing analysis of MRL: A real-time rule-based system

This paper examines issues on how to predict timing behavior of rule-based decision systems for real-time applications. In particular, we focus on the analysis of response time of rule-based programs written in the production system language MRL. The design goal of MRL is to allow programmers to write OPS5-like rule-based programs in a language that is more amenable to formal analysis based on the semantic foundation underlying the language Unity. The language MRL, its analysis algorithms, and its execution system form a package of design tools for programming real-time rule-based decision systems.This project is partly supported by research grants from Office of Naval Research under ONR contract number N00014-89-J-1472 as well as ONR contract number N000014-89-J-1913, by a grant from Texas Advance Technology Program, and also by a grant from Texas Instruments Corporation.     

A new explanation of the glitch phenomenon

Summary We consider a discrete model for asynchronous circuits and show that, under very mild restrictions, this model excludes the existence of glitch-free arbiters. This result contradicts a long standing conjecture that the nonexistence of glitch-free arbiters is due to the continuous nature of such circuits.Work supported in part by Office of Naval Research Contract N00014-89-J-1913     

A time-optimal parallel algorithm for three-dimensional convex hulls

In this paper we present an O(1/ logn)-time parallel algorithm for computing the convex hull ofn points in ³. This algorithm usesO(@#@ n^1+a) processors on a CREW PRAM, for any constant 0 < 1. So far, all adequately documented parallel algorithms proposed for this problem use time at least O(log² n). In addition, the algorithm presented here is the first parallel algorithm for the three-dimensional convex hull problem that is not based on the serial divide-and-conquer algorithm of Preparata and Hong, whose crucial operation is the merging of the convex hulls of two linearly separated point sets. The contributions of this paper are therefore (i) an O(logn)-time parallel algorithm for the three-dimensional convex hull problem, and (ii) a parallel algorithm for this problem that does not follow the traditional paradigm.This paper was presented in preliminary form at the 9th Annual ACM Symposium on Computational Geometry, San Diego, CA, May 1993 [32]. The work of N. M. Amato was supported in part by an AT&T Bell Laboratories Graduate Fellowship, the Joint Services Electronics Program (U.S. Army, U.S. Navy, U.S. Air Force) under Contract N00014-90-J-1270, and NSF Grant CCR-89-22008. This work was done while N. M. Amato was with the Department of Computer Science at the University of Illinois. The work of F. P. Preparata was supported in part by NSF Grants CCR-91-96152, CCR-91-96176, and ONR Contract N00014-91-J-4052, ARPA order 8225.     

Constraint query algebras

Constraint query languages are natural extensions of relational database query languages. A framework for their declarative specification (constraint calculi) and efficient implementation (low data complexity and secondary storage indexing) was presented in Kanellakis et al., 1995. Constraint query algebras form a procedural language layer between high-level declarative calculi and low-level indexing methods. Just like the relational algebra, this intermediate layer can be very useful for program optimization. In this paper, we study properties of constraint query algebras, which we present through three concrete examples. The dense order constraint algebra illustrates how the appropriate canonical form can simplify expensive operations, such as projection, and facilitate interaction with updates. The monotone two-variable linear constraint algebra illustrates the concept of strongly polynomial operations. Finally, the lazy evaluation of (non)linear constraint algebras illustrates how large numbers of (non)linear constraints could be implemented with only a small amount of costly symbolic processing.Paris C. Kanellakis, one of the authors of this paper, died in a tragic accident shortly after the completion of the first draft. We thank all the reviewers, whose comments were invaluable in helping us complete the work. We also thank Raghu Ramakrishnan for making a last-minute review of the final draft. Research supported by ONR Contracts N00014-94-1-1153 and N00014-91-J-4052, ARPA Order 8225, and by NSF Grant IRI-9509933.     

AE1: An extension matrix approximate method for the general covering problem

A new approach, the extension matrix approach, is introduced and used to show that some optimization problems in general covering problem areNP-hard. Approximate solutions for these problems are given. Combining these approximate solutions, this paper presents an approximately optimal covering algorithm,AE1. Implementation shows thatAE1 is efficient and gives optimal or near optimal results.This research was supported in part by the National Science Foundation under Grant DCR 84-06801, Office of Naval Research under Grant N00014-82-K-0186, Defense Advanced Research Project Agency under Grant N00014-K-85-0878, and Education Ministry of the People's Republic of China.On leave from Harbin Institute of Technology, Harbin, China.     

A criterion for atomicity

Most proof methods for reasoning about concurrent programs are based upon theinterleaving semantics of concurrent computation: a concurrent program is executed in a stepwise fashion, with only one enabled action being executed at each step. Interleaving semantics, in effect, requires that a concurrent program be executed as a nondeterministic sequential program. This is clearly an abstraction of the way in which concurrent programs are actually executed. To ensure that this is a reasonable abstraction, interleaving semantics should only be used to reason about programs with simple actions; we call such programs atomic. In this paper, we formally characterise the class of atomic programs. We adopt the criterion that a program isatomic if it can be implemented in a wait-free, serialisable manner by a primitive program. A program isprimitive if each of its actions has at most one occurrence of a shared bit, and each shared bit is read by at most one process and written by at most one process. It follows from our results that the traditionally accepted atomicity criterion, which allows each action to have at most one occurrence of a shared variable, can be relaxed, allowing programs to have more powerful actions. For example, according to our criterion, an action can read any finite number of shared variables, provided it writes no shared variable.Work supported, in part, at the University of Texas at Austin by Office of Naval Research Contract N00014-89-J-1913, and at the University of Maryland by an award from the University of Maryland General Research Board.Work supported, in part, by Office of Naval Research Contract N00014-89-J-1913.     

Optimal cooperative search in fractional cascaded data structures

Fractional cascading is a technique designed to allow efficient sequential search in a graph with catalogs of total sizen. The search consists of locating a key in the catalogs along a path. In this paper we show how to preprocess a variety of fractional cascaded data structures whose underlying graph is a tree so that searching can be done efficiently in parallel. The preprocessing takesO(logn) time withn/logn processors on an EREW PRAM. For a balanced binary tree, cooperative search along root-to-leaf paths can be done inO((logn)/logp) time usingp processors on a CREW PRAM. Both of these time/processor constraints are optimal. The searching in the fractional cascaded data structure can be either explicit, in which the search path is specified before the search starts, or implicit, in which the branching is determined at each node. We apply this technique to a variety of geometric problems, including point location, range search, and segment intersection search.An earlier version of this work appears inProceedings of the 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, July 1990, pp. 307–316. The first author's support was provided in part by National Science Foundation Grant CCR-9007851, by the U.S. Army Research Office under Grants DAAL03-91-G-0035 and DAAH04-93-0134, and by the Office of Naval Research and the Advanced Research Projects Agency under Contract N00014-91-J-4052, ARPA Order 8225. This research was performed while the second author was at Brown University. Support was provided in part by an NSF Presidential Young Investigator Award CCR-9047466, with matching funds from IBM, by National Science Foundation Grant CCR-9007851, by the U.S. Army Research Office under Grant DAAL03-91-G-0035, and by the Office of Naval Research and the Advanced Research Projects Agency under Contract N00014-91-J-4052, ARPA Order 8225.     

Extending a blackboard architecture for approximate processing

Approximate processing is an approach to real-time AI problem-solving systems in domains where there are a range of acceptable answers in terms of certainty, accuracy, and completeness. Such a system needs to evaluate the current situation, make time predictions about the likelihood of achieving current objectives, monitor the processing and pursuit of those objectives, and if necessary, choose new objectives and associated processing strategies that are achievable in the available time. In this approach, the system is performingsatisficing problem-solving, in that it is attempting to generate the best possible solutions within available time and computational resource constraints.Previously published work (Lesser, Pavlin and Durfee 1988) has dealt with this approach to real-time; however, an important aspect was not fully developed: the problem solver must be very flexible in its ability to represent and efficiently implement a variety of processing strategies. Extensions to the blackboard model of problem solving that facilitate approximate processing are demonstrated for the task of knowledge-based signal interpretation. This is accomplished by extending the blackboard model of problem solving to include data, knowledge, and control approximations. With minimal overhead, the problem solver dynamically responds to the current situation by altering its operators and state space abstraction to produce a range of acceptable answers. Initial experiments with this approach show promising results in both providing a range of processing algorithms and in controlling this dynamic system with low overhead.This work was partly supported by the Office of Naval Research under a University Research Initiative grant, number N00014-86-K-0764, NSF-CER contract DCR-8500332, and ONR contract N00014-89-J-1877.