Showing papers in "Journal of the ACM in 1983"

On Communicating Finite-State Machines

Abstract: A model of commumcations protocols based on finite-state machines is investigated. The problem addressed is how to ensure certain generally desirable properties, which make protocols \"wellformed,\" that is, specify a response to those and only those events that can actually occur. It is determined to what extent the problem is solvable, and one approach to solving it ts described. Categories and SubJect Descriptors' C 2 2 [Computer-Conununication Networks]: Network Protocols-protocol verification; F 1 1 [Computation by Abstract Devices] Models of Computation--automata; G.2.2 [Discrete Mathematics] Graph Theory--graph algoruhms; trees General Terms: Reliability, Verification Additional

On the Desirability of Acyclic Database Schemes

Abstract: A class of database schemes, called acychc, was recently introduced. It is shown that this class has a number of desirable properties. In particular, several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity. In addition, several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given, and a smaple algorithm for determining acychclty is presented. Also given are several eqmvalent characterizations of those sets M of multivalued dependencies such that M is the set of muRlvalued dependencies that are the consequences of a given join dependency. Several characterizations for a conflict-free (in the sense of Lien) set of muluvalued dependencies are provided.

Applying Parallel Computation Algorithms in the Design of Serial Algorithms

Abstract: The goal of this paper is to point out that analyses of parallelism m computational problems have practical implications even when mult~processor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for designing an efficsent serial algorithm for another problem A unified framework for cases like this is presented. Particular cases, which axe discussed in this paper, provide motivation for examining parallelism in sorting, selecuon, minimum-spanning-tree, shortest route, max-flow, and matrix multiplication problems, as well as in scheduling and locational problems.

Smallest-last ordering and clustering and graph coloring algorithms

Abstract: Smallest-last vertex ordering and prlonty search are utdlzed to show for any graph G = (IT, E) that the set of all connected subgraphs maxunal with respect to their minimum degree can be determined in O(I EI + I VI) time and 21El + O(I VI) space It is further noted that the smallest-last graph coloring algonthrn can be unplemented in O(I E I + I V[) tune, and particularly effective aspects of the resulting coloring are discussed.

Degrees of acyclicity for hypergraphs and relational database schemes

Abstract: Database schemes (winch, intuitively, are collecuons of table skeletons) can be wewed as hypergraphs (A hypergraph Is a generalization of an ordinary undirected graph, such that an edge need not contain exactly two nodes, but can instead contain an arbitrary nonzero number of nodes.) A class of "acychc" database schemes was recently introduced. A number of basic desirable propemes of database schemes have been shown to be equivalent to acyclicity This shows the naturalness of the concept. However, unlike the situation for ordinary, undirected graphs, there are several natural, noneqmvalent notions of acyclicity for hypergraphs (and hence for database schemes). Various desirable properties of database schemes are constdered and it is shown that they fall into several equivalence classes, each completely characterized by the degree of acycliclty of the scheme The results are also of interest from a purely graph-theoretic viewpomt. The original notion of aeyclicity has the countermtmtive property that a subhypergraph of an acychc hypergraph can be cyclic. This strange behavior does not occur for the new degrees of acyelicity that are considered.

Locking Primitives in a Database System

Abstract: Locking ~s a frequently used concurrency control mechamsm m database systems. Most systems offer one or more lock modes, usually read and write modes. Here, one operatwnal lock mode is assumed for each database operation, and a criterion for \"good\" lock compatibdlty functions, called maximal permtssiveness, is gtven Operatmnal modes are used as a basis to define generalized update modes that correspond to arbitrary lock conversions. The notion of intention modes from System R is extended to arbnrary lock modes, and the mteractmn among the classes of lock modes thus created is studied.

Improving the performance guarantee for approximate graph coloring

Abstract: The performance guarantee of a graph coloring algorithm is the worst case ratio between the number of colors it uses on the input graph and the chromauc number of this graph. The previous best known polynomial-time algorithm had a performance guarantee O(n/logn) for graphs on n vertices. This result stood unchallenged for eight years. This paper presents an efficient algorithm with performance guarantee of O(n(loglog n)2/(logn)2).

The Weak Byzantine Generals Problem

Abstract: The Byzantine Generals Problem requires processes to reach agreement upon a value even though some of them may fad. It is weakened by allowing them to agree upon an "incorrect" value if a failure occurs. The transaction eormmt problem for a distributed database Js a special case of the weaker problem. It is shown that, like the original Byzantine Generals Problem, the weak version can be solved only ff fewer than one-third of the processes may fad. Unlike the onginal problem, an approximate solution exists that can tolerate arbaranly many failures.

The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees

Abstract: Le graphe de voisinage relatif (RNG) d'un ensemble V de points dans un espace euclidien est un graphe (V,E) tel que (p,q) appartient a E si et seulement si il n'existe pas de point z de V tel que d(p,z)

The Expressiveness of Simple and Second-Order Type Structures

Abstract: Typed lambda (?`-) calculi provtde convement mathematical settings in which to investigate the effects of type structure on the function definmon mechamsm m programming languages. Lambda expressaons mtm~c programs that do not use while loops or carcular function definitions. Two typed ?`-calculi are investigated, the sunply typed ?`-calculus, whose types are similar to Pascal types, and the second-order typed ?,-calculus, which has a type abstractaon mechamsm simdar to that of modern data abstraction languages such as ALPHARD. Two related questions are considered for each calculus: (1) What functaons are definable m the calculus? and (2) How difficult is the proof that all expressions in the calculus are normahzable 0.e., that all computaUons termmate)* The simply typed calculus only defines elementary functtons. Normahzation for this calculus ~s provable using commonplace forms of reasoning formalazable m Peano arithmetic The second-order calculus defines a huge hierarchy of funcuons going far beyond Ackermann's function These funcuons are so rapidly increasing that Peano arithmetic cannot prove that they are total In fact, normalizataon for the second-order calculus cannot be proved even m second-order Peano artthmetic, nor m Peano anthmettc augmented by all true statements Also d~scussed are the lmphcataons of the present ?`-calculus results for the programming languages PASCAL, ALPHARD, RUSSELL, and MODEL. Categories and SubJect Descriptors: D 3.3 [Programming Languages]: Language Constructs--control structures, data types and structures; F. 1 1 [Computation by Abstract Devices]\" Models of Computation computablhty theory, F.4 1 [Mathematical Logic and Formal Languages]\" Mathematical Logic--computabzlity theory, lambda calculus and related systems General Terms Algorithms, Languages, Theory Addltaonal

Solving Linear Algebraic Equations on an MIMD Computer

Abstract: Two pracUcal parallel algorithms for solving systems of dense linear equations on an MIMD computer are presented. They are based on Gaussian elunmation and Givens transformations The algonthms are numerically stable and have been tested on the Denelcor HEP machine. Categories and SubJect Descriptors' G 1.0 ]Numerical Analysis] General--parallel algorithms; G. 1.3 [Numerical Analysis]: Numerical Linear Algebra--hnear systems General Terms\" Algorithms, Theory Addiaonal

Formulations and Algorithms for the Capacitated Minimal Directed Tree Problem

Abstract: The Capacltated Minmaal Directed Tree Problem is fundamental m many network design problems. A new linear integer programming formulauon of the problem which leads to a Dantzlg-Wolfe decomposmon and to a new Lagrangean relaxation procedure for the Capacaated Mmunal Directed Tree Problem as presented This relaxation is used for deriving tight lower bounds on the optunal solution and m heunsucs for obtaining approxtmate solutions The effectiveness of the procedure is demonstrated in computational tests Categories and SubJect Descriptors: C.2.1 [Computer-Communication Networks]: Network Architecture and Design--network topology; D 4.8 [Operating Systems]: Performance--modehng and predwtion; G 2.1 [Discrete Mathematics]: Combinatoncs--combmatorml algorithms; G.2.2 [Di~tete Mathematics]. Graph Theory--trees General Terms. Algonthrns, Management, Theory Ad&tional

Robustness of queuing network formulas

Abstract: Analyuc models of queuing networks have been observed to give good results for systems which do not conform to the assumptions of classical queuing theory This has been explained to some extent by the recently proposed concept of operational analysis However, the use of operational analysis for prediction of system performance revolves a restrictive assumption, that of homogeneous service tnnes (HST), and practical systems often deviate from HST behavior. It is shown that the main system performance measures are surpnsmgly insensitive to violations of the HST assumption. This further explains the robustness of analyacal models for predicting performance of queuing networks Some issues regarding the operational versus stochasuc approaches are resolved, since it is clatmed that the present analysis, which is carried out m the operational framework, cannot be meaningfully carried out m the stochastic framework. Categones and Subject Descnptors: D.4.8 [Operating Systems] Performance--modeling andpredtctwn; operatwnal analysis;, stochastic analysts General TermsExperimentation, Measurement, Performance Additional

Three-Dimensional VLSI: a case study

Abstract: The advantages of three-dimensional c~rcmts are studied by comparing sample three-dimensional reahzauons of certain common families of c~rcmts, namely, permutation networks, FFT circmts, and complete binary trees, with the famd~es' optunal two-dtmens~onal reahzatlons. These circuits are then used as building blocks to obtain efficient three-dimensional realizations of arbitrary circuits. The results obtained indicate (roughly) that bounds on area (both upper and lower) in the neighborhood of order n 2 m the two-dtmens~onal case translate to bounds on volume m the neighborhood of order n a/2 m the three-dimensional case. Moreover, several of the upper bounds are attainable using (idealized) realizations that have actwe devices on only one level and that use the third dimension only for wirerouting, such reahzauons place fewer demands on the fabrication technology. However, it is also shown that unrestricted use of the third dimension can y~eld reallzauons that are more conservative of volume (by the factor log~/2n) than any \"one-actwe-level\" reallzauon can be. Finally, examples are presented whereto two-dunenslonal reahzaUons reqmre dewce-to-dewce wire lengths as large as n/logn, whde eqmvalent three-dLmens~onal reahzatlons can get by w~th wire lengths not exceeding n ~/2. Thus, at least in the worst case, there are substantive savings from three-dLmens~onal circuit realizations, in both material (area versus volume) and tune (wire length) Categories and SubJect Descnptors B.2.m [Arithmetic and Logic Structures]: Miscellaneous; B.7 1 [Integrated Circuits]: Types and Design Styles--VLS1; F 2.2 [Analysis of Algorithms and Problem Complexity]. Nonnumencal Algorithms and Problems--routing and layout General Terms Design, Theory Addmonal

A Characterization of Product-Form Queuing Networks

Abstract: Sunple criterta are given for determining whether a queuing network model has a product-form solution and is thus computationally tractable Categories and SubJect Descriptors. D.4.8 [Operating Systems]: Performance--queuing theory, stochasuc analysts General Terms Performance, Theory Additional

Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs

Abstract: Let Q be any algebraic structure and ~the set of all total programs over Q using the instruction set {z ,,-1, z , , x + y, z ,,-x y , z ~ x * y , z ~-x / y } . (A program is total if no division by zero occurs during any computation ) Let the equivalence problem for ~ be the problem of deciding for two given programs in ~whether or not they compute the same funcuon The following results are proved: (1) If Q is an inftmte field (e.g, the rauonal numbers or the complex numbers), then the equwalence problem for ~ is probabilistlcally decidable in polynomml time. The result also holds for programs with no dwlslon instructions and Q an infimte integral domain (e.g., the integers). (2) If Q is a finite field, or if Q is a fimte set of integers of cardmahty _>2, then the equivalence problem is NP-hard. The case when the field Q is finite but its cardinality is a funcuon of the size of the instance to the eqmvalence problem is also considered An example is shown for which a sharp boundary between the classes NP-hard and probabihsticaUy decidable exists (provided they are not identical classes).

Graph Algorithms for Functional Dependency Manipulation

Abstract: . A graph-theoretic approach for the representation of functional dependenoes in relauonal databases is introduced and applied in the construction of algorithms for manipulating dependencies. This approach allows a homogeneous treatment of several problems (closure, minimization, etc.), which leads to simpler proofs and, m some cases, more efficient algorithms than in the current literature. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumencal Algorithms and Problems--computations on d, screte structures; G.2.2 [Diserete Mathematics]: Graph Theory--graph algorithms; H.2.1 [Database Management]: Logical Design-normal forms; schema and subschema General Terms: Algorithms, Design, Management, Theory Additional Key Words and Phrases: Closure, computational complexity, functional dependency, FD- graph, minimal coverings, relational database 1. Introduction

Cost Trade-offs in Graph Embeddings, with Applications

Abstract: An embedding of the graph G in the graph H is a one-to-one association of the vertices of G with the vertices of H. There are two natural measures of the cost of a graph embedding, namely, the dilation-cost of the embedding: the maximum distance in H between the images of vertices that are adjacent in G, and the expansion-cost of the embedding: the ratio of the size of H to the size of G. The main results of this paper illustrate three situations wherein one of these costs can be minimized only at the expense of a dramatic increase in the other cost. The first result establishes the following: there is an embedding of n-node complete ternary trees in complete binary trees with dilation-cost 2 and expansion-cost Θ(nλ) where λ=log3(4/3); but any embedding of these ternary trees in binary trees that has expansion-cost <2 must, infinitely often, have dilation-cost ⩾ (const)log log log n. The second result provides a stronger but less easily stated example of the same type of tradeoff. The third result concerns generic binary trees, that is, complete binary trees into which all n-node binary trees are "efficiently" embeddable. There is a generic binary tree into which all n-node binary trees are embeddable with dilation-cost O(1) and expansion-cost O(nc) for some fixed constant c; if one insists on embeddings whose dilation-cost is exactly 1, then these embeddings must have expansion-cost ω(n(log n)/2); if one insists on embeddings whose expansion-cost is <2, then these embeddings must, infinitely often, have dilation-cost ⩾ (const)log log log n. An interesting application of the polynomial size generic binary tree in the first part of this three-part result is to yield simplified proofs of several results concerning computational systems with an intrinsic notion of "computation tree", such as alternating and nondeterministic Turing machines and context-free grammars.

Parametric Combinatorial Computing and a Problem of Program Module Distribution

Abstract: En calcul parametrique certaines parties de la description du probleme sont donnees comme des fonctions d'un ou plusieurs parametres, pouvant varier sur un grand nombre de valeurs. Des valeurs fixes des parametres specifient un probleme particulier, l'objectif du calcul parametrique etant de resoudre de maniere efficace de tels problemes en fonction des valeurs des parametres. On propose une methode de calcul parametrique generale, efficace pour une large classe de problemes combinatoires; la methode est liee a une methode developpee par Megiddo pour la resolution de problemes d'optimisation de ratios. On traite un exemple de distribution de modules de programme d'ordinateur entre deux processeurs

Bidirectional Heuristic Search Again

Abstract: Extensive modifications of a previously published bidirectional heuristic search algorithm (see D. de Champeaux and L. Sint, IBID., vol.24, no.2, p.177-91, 1977) are presented in order to preserve the property that shortest solutions are found under appropriate circumstances. Theoretical results encompass the generalisation of the unidirectional optimality theorem. 5 references.

Search Algorithms Under Different Kinds of Heuristics—A Comparative Study

Abstract: Three heuristic search algorithms, called algorithms a, b and c, are presented. Their performance, with the admissibility condition relaxed, is compared using the following two criteria: (i) number of node expansions and (ii) cost of solution found. First, a general comparison is made. In this process some variations and extensions of c are also considered. Subsequently, two types of heuristic estimates, called proper and path dependent, are defined, and the algorithms are reexamined. It is shown that on the whole a (Nilsson's algorithm) and b (Martelli's algorithm) are inferior to c, which is a slightly modified version of b. 7 references.

Formal Justification of a Proof System for Communicating Sequential Processes

Abstract: In a previous paper a proof system dealing with partial correctness of communicating sequential processes was introduced. Soundness and relative completeness of this system are proved here. It is also indicated in what way the semantics and the proof system can be extended to deal with the total correctness of the programs.

Implicit Data Structures for the Dictionary Problem

Abstract: Several new data structures for dictionaries are presented that use just one location in addition to those required for key values. The structures are generahzations of a rotated sorted list, with the best realizing a search tune of O(log n) and insemon and deletion tunes of O(n ~ ( l o g n) 3/2) Structures adapted to allow fast average search times and structures that allow pamal match retrieval on records wRh d keys, d > 1, are also considered.

The Proof of a Folk Theorem on Queuing Delay with Applications to Routing in Networks

Abstract: It is shown that among all arrival processes (not necessarily stationary or renewal type) for an exponential server queue with specified arrival and service rates, that the arrival process which mmimizes the average delay and related quantities is the process with constant interarrival times. The proof is based on a convexity property of exponential server queues which is of independent interest. The folk theorem provides a lower bound, which is readily computable by existing methods, to the average delay in a network of queues under rather general routing disciplines. A sharper lower bound on average delay is provided for the special case of Generalized Round Robin routing for a Poisson arrival process.

Efficiency of Synchronous Versus Asynchronous Distributed Systems

Abstract: A system of parallel processes is said to be synchronous if all processes run using the same clock, and it is said to be asynchronous if each process has its own independent clock. For any s, n, a particular distributed problem is defined involving system behavior at n ports. This problem can be solved in time s by a synchronous system but requires time at least (s-1)(log/sub b/n) on any asynchronous system, where b is a constant reflecting the communication bound in the model. This appears to be the first example of a problem for which an asynchronous system is probably slower than a synchronous one, and it shows that a straightforward step-by-step and process-by-process simulation of an n-process synchronous system by an n-process asynchronous system necessarily loses a factor of log/sub b/n in speed. 1 ref.

The Time for a Round Trip in a Cycle of Exponential Queues

Abstract: In [1] Chow obtained the steady-state distribution of the cycle time of a customer in a closed tandem queue composed of two exponential FIFO servers and populated by an arbitrary fixed number of customers. The present paper gives the generalization of Chow’s result (by means of a different proof) to the case of arbitrarily many exponential servers.

Optimal Search on Some Game Trees

Abstract: It is proved that the dlrecUonal algorithm for solving a game tree is optimal, in the sense of average run trine, for balanced trees (a family containing all uniform trees). This result implies that the alpha-beta pruning method is asymptotJcally opttmal among all game searching algorithms. Categones and Subject Descriptors. 1 2.8 [Artificial Intelligence] Problem Solving, Control Methods and Search--graph and tree search strategies General Terms' None Addmonal

Computable Error Bounds for Aggregated Markov Chains

Abstract: : This paper describes a method for computing the steady state probability vector of a nearly completely decomposable Markov chain. The method is closely related to one proposed by Simon and Ando and developed by Courtois. However, the method described here does not require the determination of a completely decomposable stochastic approximation to the transition matrix and hence it is applicable to matrices other than stochastic. An error analysis of the procedure is given which results in effectively computable error bounds. (Author)

Decision Quality As a Function of Search Depth on Game Trees

Abstract: One important application of tree searching is looking ahead on a decision tree or game tree to try to predict the results of a decision. To guarantee correct results, substantial portions of the tree must be completely searched, which is physically impossible for very large trees. The author has developed a mathematical theory modeling the effects of search depth on the probability of making a correct decision. In this theory, the errors made by the evaluation function are modeled as independent, identically distributed random errors superimposed on the true values of the nodes evaluated. This research has produced the surprising result that there is an infinite class of game trees for which searching deeper does not increase the probability of making a correct decision, but instead causes the decision to become more and more random. The paper contains a mathematical proof of this statement, experimental verification of it, and a discussion of its significance. 31 references.