A note on weighted distributed match-making

In many distributed computing environments, processes are concurrently executed by nodes in a store-and-forward network. Distributed control issues as diverse as name-server, mutual exclusion, and replicated data management, involve making matches between processes. The generic paradigm is a formal problem called “distributed match-making.” We define multidimensional and weighted versions, and the relations between the two, and develop a very general method to prove lower bounds on the complexity as a tradeoff between number of messages and “distributedness.” The resulting lower bounds are tight in all cases we have examined. We present a success-stop version of distributed match-making that is analysed in terms of a weight distribution that in all cases results in approximately halving the (expected) number of messages required in the corresponding strategy that does not use these weights. The second author did part of this work at the Laboratory for Computer Science, M.I.T., Cambridge, MA. He was supported in part by the Office of Naval Research under Contract N00014-85-K-0168, by the Office of Army Research under Contract DAAG29-84-K-0058, by the National Science Foundation under Grant DCR-83-02391, and by the Defence Advanced Research Projects Agency (DARPA) under Contract N00014-83-K-0125. A preliminary version of this paper appeared inProc. VLSI Algorithms and Architectures, 3rd Aegean Workshop on Computing (AWOC 88), Lecture Notes in Computer Science, vol. 319, Springer-Verlag, Berlin, 1988, pp. 361–368.     

Topological numbering of features on a mesh

Assume we are given ann ×n binary image containing horizontally convex features; i.e., for each feature, each of its row's pixels form an interval on that row. In this paper we consider the problem of assigning topological numbers to such features, i.e., assign a number to every featuref so that all features to the left off in the image have a smaller number assigned to them. This problem arises in solutions to the stereo matching problem. We present a parallel algorithm to solve the topological numbering problem inO(n) time on ann ×n mesh of processors. The key idea of our solution is to create a tree from which the topological numbers can be obtained even though the tree does not uniquely represent the to the left of relationship of the features.The work of M. J. Atallah was supported by the Office of Naval Research under Grants N00014-84-K-0502 and N00014-86-K-0689, and the National Science Foundation under Grant DCR-8451393, with matching funds from AT&T. Part of this work was done while he was a Visiting Scientist at the Center for Advanced Architectures project of the Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffett Field, CA 94035, USA. S. E. Hambrusch's work was supported by the Office of Naval Research under Contracts N00014-84-K-0502 and N00014-86K-0689, and by the National Science Foundation under Grant MIP-87-15652. Part of this work was done while she was visiting the International Computer Science Institute, Berkeley, CA 94704, USA. The work of L. E. TeWinkel was supported by the Office of Naval Research under Contract N00014-86K-0689.     

Communication-efficient parallel algorithms for distributed random-access machines

This paper introduces a model for parallel computation, called thedistributed randomaccess machine (DRAM), in which the communication requirements of parallel algorithms can be evaluated. A DRAM is an abstraction of a parallel computer in which memory accesses are implemented by routing messages through a communication network. A DRAM explicitly models the congestion of messages across cuts of the network.We introduce the notion of aconservative algorithm as one whose communication requirements at each step can be bounded by the congestion of pointers of the input data structure across cuts of a DRAM. We give a simple lemma that shows how to shortcut pointers in a data structure so that remote processors can communicate without causing undue congestion. We giveO(lgn)-step, linear-processor, linear-space, conservative algorithms for a variety of problems onn-node trees, such as computing treewalk numberings, finding the separator of a tree, and evaluating all subexpressions in an expression tree. We giveO(lg² n)-step, linear-processor, linear-space, conservative algorithms for problems on graphs of sizen, including finding a minimum-cost spanning forest, computing biconnected components, and constructing an Eulerian cycle. Most of these algorithms use as a subroutine a generalization of the prefix computation to trees. We show that any suchtreefix computation can be performed inO(lgn) steps using a conservative variant of Miller and Reif's tree-contraction technique.This research was supported in part by the Defense Advanced Research Projects Agency under Contract N00014-80-C-0622 and by the Office of Naval Research under Contract N00014-86-K-0593. Charles Leiserson is supported in part by an NSF Presidential Young Investigator Award with matching funds provided by AT&T Bell Laboratories and Xerox Corporation. Bruce Maggs is supported in part by an NSF Fellowship.     

Maximum queue size and hashing with lazy deletion

We answer questions about the distribution of the maximum size of queues and data structures as a function of time. The concept of maximum occurs in many issues of resource allocation. We consider several models of growth, including general birth-and-death processes, the M/G/ model, and a non-Markovian process (data structure) for processing plane-sweep information in computational geometry, called hashing with lazy deletion (HwLD). It has been shown that HwLD is optimal in terms of expected time and dynamic space; our results show that it is also optimal in terms of expectedpreallocated space, up to a constant factor.We take two independent and complementary approaches: first, in Section 2, we use a variety of algebraic and analytical techniques to derive exact formulas for the distribution of the maximum queue size in stationary birth-and-death processes and in a nonstationary model related to file histories. The formulas allow numerical evaluation and some asymptotics. In our second approach, in Section 3, we consider the M/G/ model (which includes M/M/ as a special case) and use techniques from the analysis of algorithms to get optimal big-oh bounds on the expected maximum queue size and on the expected maximum amount of storage used by HwLD in excess of the optimal amount. The techniques appear extendible to other models, such as M/M/1.Research was also done while the author was at Princeton University, supported in part by a Procter Fellowship.Research was also done while the author was on sabbatical at INRIA in Rocquencourt, France, and at Ecole Normale Supérieure in Paris, France. Support was provided in part by National Science Foundation Research Grant DCR-84-03613, by an NSF Presidential Young Investigator Award with matching funds from an IBM Faculty Development Award and an AT&T research grant, by a Guggenheim Fellowship, and by the Office of Naval Research and the Defense Advanced Research Projects Agency under Contract N00014-83-K-0146 and ARPA Order 6320, Amendment 1.     

Optimal randomized parallel algorithms for computational geometry

We present parallel algorithms for some fundamental problems in computational geometry which have a running time ofO(logn) usingn processors, with very high probability (approaching 1 asn ). These include planar-point location, triangulation, and trapezoidal decomposition. We also present optimal algorithms for three-dimensional maxima and two-set dominance counting by an application of integer sorting. Most of these algorithms run on a CREW PRAM model and have optimal processor-time product which improve on the previously best-known algorithms of Atallah and Goodrich [5] for these problems. The crux of these algorithms is a useful data structure which emulates the plane-sweeping paradigm used for sequential algorithms. We extend some of the techniques used by Reischuk [26] and Reif and Valiant [25] for flashsort algorithm to perform divide and conquer in a plane very efficiently leading to the improved performance by our approach.This is a substantially revised version of the paper that appeared as Optimal Randomized Parallel Algorithms for Computational Geometry in theProceedings of the 16th International Conference on Parallel Processing, St. Charles, Illinois, August 1987.This research was supported by DARPA/ARO Contract DAAL03-88-K-0195, Air Force Contract AFOSR-87-0386, DARPA/ISTO Contracts N00014-88-K-0458 and N00014-91-J-1985, and by NASA Subcontract 550-63 of Primecontract NAS5-30428.     

The instability of self-stabilization

Summary We argue that the important property of self-stabilization is, in principle, unstable across system classes. In particular, we first define a very broad notion of simulation. We then define what it means for a simulation to either preserve or force self-stabilization. Given these definitions, we then show that, for a variety of system classes, there is no simulation that preserves or forces self-stabilization.This work was supported in part by U.S. Office of Naval Research Grant No. N00014-86-K-0763 and National Science Foundation Grant No. CCR-8711579. Preliminary versions of this work have appeared in the Proceedings of the MCC Workshop on Self-Stabilizing Systems, MCC Technical Report No. STP-379-89, Austin, Texas, August 1989, and under the title System Simulation and the Sensitivity of Self-Stabilization in the Proceedings of the 14th International Symposium on Mathematical Foundations of Computer Science, LNCS 379, pp. 249–258, Porabka-Kozubnik, Poland, August–September 1989.     

Arguments and cases: An inevitable intertwining

We discuss several aspects of legal arguments, primarily arguments about the meaning of statutes. First, we discuss how the requirements of argument guide the specification and selection of supporting cases and how an existing case base influences argument formation. Second, we present,our evolving taxonomy of patterns of actual legal argument. This taxonomy builds upon our much earlier work on argument moves and also on our more recent analysis of how cases are used to support arguments for the interpretation of legal statutes. Third, we show how the theory of argument used by CABARET, a hybrid case-based/rule-based reasoner, can support many of the argument patterns in our taxonomy.This work was supported in part by the National Science Foundation, contract IRI-890841, the Air Force Office of Sponsored Research under contract 90-0359, the Office of Naval Research under a University Research Initiative Grant, contract N00014-87-K-0238, and a grant from GTE Laboratories, Inc., Waltham, Mass.     

The complexity of planar compliant motion planning under uncertainty

We consider the computational complexity of planning compliant motions in the plane, given geometric bounds on the uncertainty in sensing and control. We can give efficient algorithms for generating and verifying compliant motion strategies that are guaranteed to succeed as long as the sensing and control uncertainties lie within the specified bounds. We also consider the case where a compliant motion plan is required to succeed over some parametric family of geometries. While these problems are known to be intractable in three dimensions, we identify tractable subclasses in the plane.This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the Laboratory's Artificial Intelligence research is provided in part by the Office of Naval Research under Office of Naval Research Contract N00014-81-K-0494 and in part by the Advanced Research Projects Agency under Office of Naval Research Contracts N00014-85-K-0124 and N00014-82-K.-0334. The author was funded in part by a NASA fellowship administered by the Jet Propulsion Laboratory, and in part by the Mathematical Sciences Institute and the National Science Foundation.     

An improved technique for output-sensitive hidden surface removal

We derive a new output-sensitive algorithm for hidden surface removal in a collection ofn triangles, viewed from a pointz such that they can be ordered in an acyclic fashion according to their nearness toz. Ifk is the combinatorial complexity of the outputvisibility map, then we obtain a sophisticated randomized algorithm that runs in (randomized) timeO(n^4/3 log^2.89 n +k ^3/5 n ^{4/5 +} for any > 0. The method is based on a new technique for tracing the visible contours using ray shooting.Work by the first author was partially supported by the ESPRIT II Basic Research Actions Program of the EC, under Contract No. 3075 (project ALCOM). Work by the second author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the NCRD-the Israeli National Council for Research and Development-and the Fund for Basic Research in Electronics, Computers, and Communication administered by the Israeli Academy of Sciences. A preliminary version of this paper appeared as part of the conference proceedings paper [17].     

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.     

Algorithms for parallel memory,II: Hierarchical multilevel memories

In this paper we introduce parallel versions of two hierarchical memory models and give optimal algorithms in these models for sorting, FFT, and matrix multiplication. In our parallel models, there areP memory hierarchies operating simultaneously; communication among the hierarchies takes place at a base memory level. Our optimal sorting algorithm is randomized and is based upon the probabilistic partitioning technique developed in the companion paper for optimal disk sorting in a two-level memory with parallel block transfer. The probability of using/times the optimal running time is exponentially small in (log ) logP.A summarized version of this research was presented at the 22nd Annual ACM Symposium on Theory of Computing, Baltimore, MD, May 1990. This work was done while the first author was at Brown University. Support was provided in part by a National Science Foundation Presidential Young Investigator Award with matching funds from IBM, by NSF Research Grants DCR-8403613 and CCR-9007851, by Army Research Office Grant DAAL03-91-G-0035, and by the Office of Naval Research and the Defense Advanced Research Projects Agency under Contract N00014-91-J-4052 ARPA Order 8225. This work was done in part while the second author was at Brown University supported by a Bellcore graduate fellowship and at Bellcore.     

Using mappings to prove timing properties

Summary A new technique for proving timing properties for timing-based algorithms is described; it is an extension of the mapping techniques previously used in proofs of safety properties for asynchronous concurrent systems. The key to the method is a way of representing a system with timing constraints as an automaton whose state includes predictive timing information. Timing assumptions and timing requirements for the system are both represented in this way. A multi-valued mapping from the assumptions automaton to the requirements automaton is then used to show that the given system satisfies the requirements. One type of mapping is based on a collection of progress functions providing measures of progress toward timing goals. The technique is illustrated with two examples, a simple resource manager and a two-process race system. Nancy A. Lynch received the B.S. degree in mathematics from Brooklyn College, Brooklyn, NY, in 1968, and the Ph.D. degree in mathematics from the Massachusetts Institute of Technology, Cambridge, MA, in 1972. She is presently a professor of computer science and electrical engineering at Massachusetts Institute of Technology. She has also been on the computer science faculty at Georgia Institute of Technology and on the mathematics faculty at Tufts University and the University of Southern California. Her research interests are in distributed and real-time computing and theoretical computer science. In particular, she has worked on formal models and verification methods, on algorithm design and analysis, and on impossibility results. She also likes to hike and ski. Hagit Attiya received the B.Sc. degree in Mathematics and Computer Science from the Hebrew University of Jerusalem, in 1981, the M.Sc. and Ph.D. degrees in Computer Science from the Hebrew University of Jerusalem, in 1983 and 1987, respectively. She is presently a senior lecturer at the department of Computer Science at the Technion, Israel Institute of Technology. Prior to this, she has been a post-doctoral research associate at the Laboratory for Computer Science at M.I.T. Her general research interests are distributed computation and theoretical computer science. More specific interests include fault-tolerance, timing-based and asynchronous algorithms.This work was supported by ONR contracts N00014-85-K-0168 and N00014-91-J-1046, by NSF grants CCR-8611442 and CCR-8915206, and by DARPA contracts N00014-87-K-0825 and N00014-89-J-1988     

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].     

Asymptotically optimal algorithms for approximate agreement

This paper introduces some algorithms to solve crash-failure, failure-by-omission and Byzantine failure versions of the Byzantine Generals or consensus problem, where non-faulty processors need only arrive at values that are close together rather than identical. For each failure model and each value ofS, we give at-resilient algorithm usingS rounds of communication. IfS=t+1, exact agreement is obtained. In the algorithms for the failure-by-omission and Byzantine failure models, each processor attempts to identify the faulty processors and corrects values transmited by them to reduce the amount of disagreement. We also prove lower bounds for each model, to show that each of our algorithms has a convergence rate that is asymptotic to the best possible in that model as the number of processors increases. Alan Fekete was born in Sydney Australia in 1959. He studied Pure Mathematics and Computer Science at the University of Sydney, obtaining a B.Sc.(Hons) in 1982. He then moved to Cambridge, Massachusetts, where he obtained a distributed Ph.D. degree, awarded by Harvard University's Mathematics department for work supervised by Nancy Lynch in M.I.T.'s Laboratory for Computer Science. He spend the year 1987–1988 at M.I.T. as a postdoctoral Research Associate, and is now Lecturer in Computer Science at the University of Sydney. His research concentrates on understanding the modularity in distributed algorithms, especially those used for concurrency control in distributed databases.A preliminary version of this paper has appeared in the Proceedings of the 5th ACM Symposium on Principles of Distributed Computing (August 1986). This work was begun in the Department of Mathematics, Harvard University, and completed at the Laboratory for Computer Science at Massachusetts Institute of Technology. The work was supported in part (through Professor N. Lynch) by the Office of Naval Research under Contract N00014-85-K-0168, by the Office of Army Research under contract DAAG29-84-K-0058, by the National Science Foundation under Grants MCS-8306854, DCR-83-02391, and CCR-8611442, and by the Defense Advanced Research Projects Agency (DARPA) under Contract N00014-83-K-0125     

Parallel construction of a suffix tree with applications

Many string manipulations can be performed efficiently on suffix trees. In this paper a CRCW parallel RAM algorithm is presented that constructs the suffix tree associated with a string ofn symbols inO(logn) time withn processors. The algorithm requires (n ²) space. However, the space needed can be reduced toO(n ¹⁺) for any 0< 1, with a corresponding slow-down proportional to 1/. Efficient parallel procedures are also given for some string problems that can be solved with suffix trees.The results of this paper have been achieved independently and simultaneously in [AI-86] and [LSV-86]. The research of U. Vishkin was supported by NSF Grant NSF-CCR-8615337, ONR Grant N00014-85-K-0046, and Foundation for Research in Electronics, Computers, and Communication, administered by the Israeli Academy of Sciences and Humanities. The research of A. Apostolico was carried out in part while visiting at the Istituto di Analisi dei Sistemi e Informatica, Rome, with support from the Italian National Research Council. The research of G. M. Landau, B. Schieber, and U. Vishkin was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under Contract DE-AC02-76ER03077.     

Efficiency of semisynchronous versus asynchronous networks

Thes-session problem is studied inasynchronous andsemisynchronous networks. Processes are located at the nodes of an undirected graphG and communicate by sending messages along links that correspond to the edges ofG. A session is a part of an execution in which each process takes at least one step; an algorithm for thes-session problem guarantees the existence of at leasts disjoint sessions. The existence of many sessions guarantees a degree of interleaving which is necessary for certain computations. It is assumed that the (real) time for message delivery is at mostd. In the asynchronous model it is assumed that the time between any two consecutive steps of any process is in the interval [0, 1]; in the semisynchronous model the time between any two consecutive steps of any process is in the interval [c, 1] for somec such that 0 <c 1,the synchronous model being the special case wherec = 1. All processes are initially synchronized and take a step at time 0.For the asynchronous model, an upper bound ofdiam(G)(d + l)(s – 1) and a lower bound ofdiam(G)d(s – 1) are presented;diam(G) is thediameter ofG. For the semisynchronous model, an upper bound of 1 + min{1/c + 1,diam(G)(d + 1)}(s – 2) is presented. The main result of the paper is a lower bound of 1 + min{1/2c,diam(G)d}(s – 2) for the time complexity of any semisynchronous algorithm for thes-session problem, under the assumption thatd (d/min{1/2c, diam(G)d}) + 2. These results imply a time separation between semisynchronous (in particular, synchronous) and asynchronous networks. Similar results are proved for the case where delays are not uniform.A preliminary version of this paper appeared in theProceedings of the 28th Annual Allerton Conference on Communication, Control, and Computing, October 1990, pp. 578–587. H. Attiya was partially supported by B. and G. Greenberg Research Fund (Ottawa) and by Techion V.P.R. funds. Part of this work was performed when she was at the Laboratory for Computer Science, MIT, supported by ONR Contract N00014-85-K-0168, by NSF Grant CCR-8915206, and by DARPA Contract N00014-87-K-0825. M. Mavronicolas was supported by ONR Contract N00014-91-J-1981. His current address is: Department of Computer Science, University of Cyprus, Cyprus, and Institute of Computer Science, Foundation of Research and Technology, Hellas, Greece.     

Interval routing schemes

In this paper the problem of routing messages along shortest paths in a distributed network without using complete routing tables is considered. In particular, the complexity of deriving minimum (in terms of number of intervals) interval routing schemes is analyzed under different requirements. For all the cases considered NP-hardness proofs are given, while some approximability results are provided. Moreover, relations among the different cases considered are studied.This work was supported by the EEC ESPRIT II Basic Research Action Program under Contract No. 7141 Algorithms and Complexity II, by the EEC Human Capital and Mobility MAP project, and by the Italian MURST 40% project Algoritmi, Modelli di Calcolo e Strutture Informative.     

A partial equivalence between shared-memory and message-passing in an asynchronous fail-stop distributed environment

This paper presents a schematic algorithm for distributed systems. This schematic algorithm uses a black-box procedure for communication, the output of which must meet two requirements: a global-order requirement and a deadlock-free requirement. This algorithm is valid in any distributed system model that can provide such a communication procedure that complies with these requirements. Two such models exist in an asynchronous fail-stop environment: one in the shared-memory model and one in the message-passing model. The implementation of the block-box procedure in these models enables us to translate existing algorithms between the two models whenever these algorithms are based on the schematic algorithm.We demonstrate this idea in two ways. First, we present a randomized algorithm for the consensus problem in the message-passing model based on the algorithm of Aspnes and Herlihy [AH] in the shared-memory model. This solution is the fastest known randomized algorithm that solves the consensus problem against a strong fail-stop adversary with one-half resiliency. Second, we solve the processor renaming problem in the shared-memory model based on the solution of Attiyaet al. [ABD⁺] in the message-passing model. The existence of the solution to the renaming problem should be contrasted with the impossibility result for the consensus problem in the shared-memory model [CIL], [DDS], [LA].A preliminary version of this paper, Shared-Memory vs. Message-Passing in an Asynchronous Distributed Environment, appeared inProc. 8th ACM Symp. on Principles of Distributed Computing, pp. 307–318, 1989. Part of this work was done while A. Bar-Noy visited the Computer Science Department, Stanford University, Stanford, CA 94305, USA, and his research was supported in part by a Weizmann fellowship, by Contract ONR N00014-88-K-0166, and by a grant of Stanford's Center for Integrated Systems.     

Multi-stack-counter languages

A stack-counter acceptor is a stack acceptor in which the storage alphabet is just one letter. The present paper discusses multi-stack-counter acceptors operating in quasirealtime, i.e., acceptors in which each storage tape is a stack counter and in which there are only a bounded number of consecutive-moves. For each positive integerk let be the family of languages accepted byk-stack-counter acceptors (k-counter acceptors). Each is a principal AFL closed under reversal but not under-free substitution or under intersection. Also, and a specific language in each, is exhibited. For each and there are noi andj such that. It is shown that a quasi-real-timek-stackcounter acceptor is equivalent to one operating in non-deterministic real time. Lastly, it is shown that acceptance by final state of ak-stack-counter acceptor is equivalent to acceptance by empty tape and final state.Also formerly with System Development Corporation, Santa Monica, California. Research sponsored in part by the Air Force Cambridge Research Laboratories, Office of Aerospace Research, USAF, under Contract F19628-70-C-0023; by the Air Force Office of Scientific Research, Office of Aerospace Research, USAF, under AFOSR No. F44620-70-C-0013; and by NSF Grant No. GJ454.