To-Yat Cheung

Graph Traversal Techniques and the Maximum Flow Problem in Distributed Computation

This paper shows that graph traversal techniques have fundamental differences between serial and distributed computations in their behaviors, computational complexities, and effects on the design of graph algorithms. It has three major parts. Section I describes the computational environment for the design and description of distributed graph algorithms in terms of an architectural model for message exchanges. The computational complexity is measured in terms of the number of messages transmitted. Section II presents several distributed algorithms for the pure traversal, depth-first search, and breadth-first search techniques. Their complexities are also given. Through these descriptions are brought out some of the intrinsic differences in the behaviors and complexities of the fundamental traversal techniques between a serial and a distributed computation environment. Section III gives the distributed version of the Ford and Fulkerson algorithm for the maximum flow problem by means of depth-first search, the largest-augmentation search and breadth-first search. The complexities of these methods are found to be 0(f*|A|), 0((l + logM/(M-1)f*|V||A|) and O(|V|6), respectively, where f* is the maximum flow value of the problem, M is the maximum number of ucs in a cut, |V| is the number of vertices, and |A| is the number of arcs. Lastly, it is shown that the largest augmentation search may be a better method than the other two. This is contrary to the known results in serial computation.

Estimating block accesses and number of records in file management

We consider the problems of estimating the number of secondary storage blocks and the number of distinct records accessed when a transaction consisting of possibly duplicate requested records is presented to a file management system. Our main results include (1) a new formula for block access estimation for the case where the requested records may have duplications and their ordering in immaterial and (2) a simple formula for estimating the number of distinct records in the transaction.

Computational Comparison of Eight Methods for the Maximum Network Flow Problem

There exist two approaches for solving the maximum network flow problem. In the fLrst approach, flow is augmented along paths and is always conserved at the vertmes In the second approach, flow is augmented through layers and is sometimes not conserved at some of the vertices. Many methods based on these two approaches are first briefly revmwed A computational comparison is then presented of eight of the methods--depth-first search, breadth-fLrst search, largestaugmentatmn, Dmic, layer-updating, Karzanov, Dimc-Karzanov, and Kinanwala-Rao. Problems with up to 1500 vertices and 7960 arcs have been tested. Computatmnal results show that Dnucs method is better than all of the other methods. However, for small-sized problems (up to 25 vertices and 200 arcs), the performances of the depth-first and breadth-first methods are comparable to Dinics method. Hence, with programming simphclty and memory space requirements taken into consideration, the former also seem to be a good chome for small problems.

A Method for Equijoin Queries in Distributed Relational Databases

A simple and efficient method for processing general equijoin queries in a distributed relational database is described. The query is first decomposed into a set of simple queries, each being involved with only one of the joining domains and its relevant equijoins. An extended version of Hevner and Yaos STRATEGY PARALLEL or STRATEGY SERIAL is then applied on each of them for generating transmission schedules. These schedules will fully reduce (with respect to a simple query) some specified relations. The latter are then transmitted to the result site for final processing. In the case of minimizing total time, our method has a lower order of complexity than ALGORITHM GENERAL studied by Hevner and Apers. Examples show that our method gives better and more efficient solutions than theirs.

A new distributed breadth-first-search algorithm

Abstract A new distributed breadth-first-search algorithm for graphs is presented. Its worst-case communication and time complexities are both O(|V|2), where |V| is the number of vertices. The existing algorithm, due to Cheung (1983), has communication and time complexities O(|V|3) and O(|V|), respectively.

Multifacility Location Problem with Rectilinear Distance by the Minimum-Cut Approach

This paper consists of two parts The first part describes an algorithm for solving the multifacility location problem with rectilinear distance, usmg a mmm]tml-cut approach. The second part is a Fortran program of this algorithm

An algorithm with decentralized control for sorting files in a network

Abstract An iterative algorithm with decentralized control for sorting a file distributed over a network is presented. In each iteration, one station assembles a sorted subfile. Each station starts by requesting from the others a certain number of keys which are below an adaptive upper bound. The requests are repeated until the station has collected enough appropriate keys for its subfile. Control is then shifted to another station for the next iteration. Simple methods are provided for determining these numbers and bounds. For a file with N records distributed over d stations, the algorithm has worst-case total message and traffic complexities O(d3) and O(d2N), respectively. In the average case, its total traffic complexity is O(N+ d2 · log(N)). The main advantage of our decentralized algorithm is that traffic burden is dispersed among all stations instead of concentrating on one of them, as in Wegners and Rotems centralized algorithms.

Recognizing different types of beta-cycles in a database scheme

Abstract This paper first distinguishes between three types of beta-cycles, namely pure beta-cycles, beta-triangles and non-pure beta-cycles. An algorithm is then proposed for detecting their presence or absence in a database scheme. The database scheme is beta-acyclic if all of them are absent. The complexity of the algorithm is O (| N | | E | 2 ), where | N | is the total number of attributes and | E | is the number of non-empty pairwise intersections of the relation of schemes. The algorithm may be used to obtain a beta-acyclic scheme through a transformation process that eliminates beta-cycles from a database scheme by suitably adding attributes into its relation schemes.

A functional network model for analytical file management in ISDN systems from generalization of videotex systems

Abstract A network is proposed as a foundation for the functional and analytical studies of ISDN systems. Based on the characteristics of the problem to be solved, the model may be used to produce a functional classification of ISDN systems so as to facilitate the research for analytical methods of solution. The model consists of two parts. Part I is a functional architecture for interconnecting the four component systems of an ISDN system, namely the systems of users, information providers, gateway service providers and information servers. Part II describes a general scheme for obtaining functional classifications of ISDN systems. Each classification depends on the functional decomposition of some of the component systems and on the processing strategies of the problem. As illustrative examples, videotex systems (which are special cases of ISDN systems) are used throughout the paper. The major videotex systems are first classified into six types. Analytical methods for solving the problems of allocation of files and assignments of users and information providers to the information servers are then discussed.

Algorithm 558: A Program for the Multifacility Location Problem with Rectilinear Distance by the Minimum-Cut Approach [H]

DESCRIPTION This algorithm complements [1], where more details are given. The coding of the algorithm consists of two subroutines, LOCATE and NETFLO. A users program calls LOCATE, which contains the major coding, and calls NETFLO for solving the minimum-cut network flow subproblems.