Tiko Kameda

On the optimal nesting order for computing N -relational joins

Using the nested loops method, this paper addresses the problem of minimizing the number of page fetches necessary to evaluate a given query to a relational database. We first propose a data structure whereby the number of page fetches required for query evaluation is substantially reduced and then derive a formula for the expected number of page fetches. An optimal solution to our problem is the nesting order of relations in the evaluation program, which minimizes the number of page fetches. Since the minimization of the formula is NP-hard, as shown in the Appendix, we propose a heuristic algorithm which produces a good suboptimal solution in polynomial time. For the special case where the input query is a “tree query,” we present an efficient algorithm for finding an optimal nesting order.

How to learn an unknown environment. I: the rectilinear case

We consider the problem faced by a robot that must explore and learn an unknown room with obstacles in it. We seek algorithms that achieve a bounded ratio of the worst-case distance traversed in order to see all visible points of the environment (thus creating a map), divided by the optimum distance needed to verify the map, if we had it in the beginning. The situation is complicated by the fact that the latter off-line problem (the problem of optimally verifying a map) is NP-hard. Although we show that there is no such “competitive” algorithm for general obstacle courses, we give a competitive algorithm for the case of a polygonal room with a bounded number of obstacles in it. We restrict ourselves to the rectilinear case, where each side of the obstacles and the room is parallel to one of the coordinates, and the robot must also move either parallel or perpendicular to the sides. (In a subsequent paper, we will discuss the extension to polygons of general shapes.) We also discuss the off-line problem for simple rectilinear polygons and find an optimal solution (in the L1 metric) in polynomial time, in the case where the entry and the exit are different points.

How to learn an unknown environment

The authors consider the problem faced by a newborn that must explore and learn an unknown room with obstacles in it. They seek algorithms that achieve a bounded ratio of the worst-case distance traversed in order to see all visible points of the environment (thus creating a map), divided by the optimum distance needed to verify the map. The situation is complicated by the fact that the latter offline problem (optimally verifying a map) is NP-hard and thus must be solved approximately. Although the authors show that there is no such competitive algorithm for general obstacle courses, they give a competitive algorithm for the case of a polygonal room with a bounded number of obstacles in it.<<ETX>>

A theory of coteries: mutual exclusion in distributed systems

A coterie under a ground set U consists of subsets (called quorums) of U such that any pair of quorums intersect with each other. Nondominated (ND) coteries are of particular interest, since they are optimal in some sense. By assigning a Boolean variable to each element in U, a family of subsets of U is represented by a Boolean function of these variables. The authors characterize the ND coteries as exactly those families which can be represented by positive, self-dual functions. In this Boolean framework, it is proved that any function representing an ND coterie can be decomposed into copies of the three-majority function, and this decomposition is representable as a binary tree. It is also shown that the class of ND coteries proposed by D. Agrawal and A. El Abbadi (1989) is related to a special case of the above binary decomposition, and that the composition proposed by M.L. Neilsen and M. Mizuno (1992) is closely related to the classical Ashenhurst decomposition of Boolean functions. A number of other results are also obtained. The compactness of the proofs of most of these results indicates the suitability of Boolean algebra for the analysis of coteries. >

Computing on an anonymous network

A network consists of a set of processors and a set of communication links connecting pairs of processors. ln the past, dozens of papers have been written on the subject of efficient distributed algorithms for various problems about networks, including leader election, spanning tree construction, and topology recognition (i.e., the determination of network topology), under the assumption tbat each processor has a unique identity number.

A diagnosing algorithm for networks

Consider a network G of n units, each of which can be tested by those units from which there is a test connection. The outcome of each test is binary (good or faulty) and is the judgment of the testing unit on the tested unit. We present an algorithm for identifying the minimum number of faulty units based on the test outcomes. It works in time proportional to τ(G)m, provided the number of faulty units is no more than τ(G), where m is the number of test connections and τ(G) is a parameter of G such that if the number of faulty units is no more than τ(G), then they are uniquely identifiable.

An improved third normal form for relational databases

In this paper, we show that some Codd third normal form relations may contain “superfluous” attributes because the definitions of transitive dependency and prime attribute are inadequate when applied to sets of relations. To correct this, an improved third normal form is defined and an algorithm is given to construct a set of relations from a given set of functional dependencies in such a way that the superfluous attributes are guaranteed to be removed. This new normal form is compared with other existing definitions of third normal form, and the deletion normalization method proposed is shown to subsume the decomposition method of normalization.

An Approach to the Diagnosability Analysis of a System

System diagnosis is investigated along the line of a pioneering work by Preparata et al. and motivated by a recent work of Hakimi and Amin. It is shown that practically all the previous results on the analysis aspect of this problem can be derived from a single theorem in this correspondence.

Scheduling to Minimize Maximum Cumulative Cost Subject to Series-Parallel Precedence Constraints

Consider a set of events that are constrained by a certain precedence relation. Associated with each event is a cost an integer, which may be interpreted as an additional number of resource units necessary for the event to occur units are released if the cost is negative. It is desired to order the events into a single sequence in such a way that the maximum cumulative cost encountered largest number of resource units used at one time is minimized. It is known that this problem is in general NP-complete. For the special case where the precedence constraints can be represented by a series-parallel graph, we present an algorithm for finding an optimal schedule whose running time does not grow faster than the square of the number of events.

Estimating testing effectiveness of the circular self-test path technique

The effectiveness of a random built-in self-test technique for VLSI circuits is studied. This technique, called the circular self-test path (CSTP), is applicable to circuits that consist of combinational blocks and registers. In particular, the effectiveness of test pattern generation, the effectiveness of test response compaction and fault coverage are examined. The test generation effectiveness is evaluated by the fraction of all possible test patterns applied during a testing session to the circuit under test. The compaction effectiveness of the CSTP technique is measured by the probability of aliasing, and fault coverage by the fraction of all permanent faults that are detected. For all these measures, simple formulas are developed, which give very accurate estimations without detailed circuit simulation. To demonstrate their accuracy, the estimates obtained by the formulas are compared to the results obtained by extensive simulation experiments. >