A tag-partitioned join algorithm is described. The algorithm partitions only one relation, while other partition-based algorithms partition both relations. It is performed as the joinable tuples of one relation are rearranged and some of them are duplicated according to the original sequence of the join attribute values of the other relation. To do this, the algorithm first finds the positions of all the tuples of the other relation which are joinable with each tuple of one relation, and then partitions joinable tuples of one relation into buckets by using the positions found. Final joining is performed on the partitioned relation and the other relation. We analyze and compare the performance of the algorithm with that of other partition-based join algorithms. The comparison shows that our method is better than other partition-based methods under the practical values of the analysis parameters.

Artificial neurons and neural networks have been shown to perform Principal Component Analysis (PCA) when gradient ascent learning rules are used, which are related to the constrained maximization of statistical objective functions. Due to their parallelism and adaptivity to input data, such algorithms and their implementations in neural networks are potentially useful in feature extraction and data compression. In the companion paper(9), two such learning rules were derived from two criteria, the Subspace Criterion and the Weighted Subspace Criterion. It was shown that the only solutions to the latter problem are dominant eigenvectors of the data covariance matrix, which are the basis vectors of PCA. It was suggested by a simulation that the corresponding learning algorithm converges to these eigenvectors. A homogeneous neural network implementation was proposed for the algorithm. The learning algorithm is analyzed here in detail and it is shown that it can be approximated by a continuous-time differential equation that is obtained by averaging. It is shown that the asymptotically stable limits of this differntial equation are the eigenvectors. The neural network learning algorithm is further extended to a case in which each neuron has a sigmoidal nonlinear feedback activity function. Then no parameters specific to each neuron are needed, and the learning rule is fully homogeneous.

Principal Component Analysis (PCA) is a useful technique in feature extraction and data compression. It can be formulated as a statistical constrained maximization problem, whose solution is given by unit eigenvectors of the data covariance matrix. In a practical application like image compression, the problem can be solved numerically by a corresponding gradient ascent maximization algorithm. Such on-line algoritms can be good alternatives due to their parallelism and adaptivity to input data. The algorithms can be implemented in a local and homogeneous way in learning neural networks. One example is the Subspace Network. It is a regular layer of parallel artificial neurons with a learning rule that is completely homogeneous with respect to the neurons. However, due to the complete homogeneity, the learning rule does not converge to the unique basis given by the dominant eigenvectors, but any basis of this eigenvector subspace is possible. In many applications like data compression, the subspace is not sufficient but the actual eigenvectors or PCA coefficient vectors are needed. A new criterion, called the Weighted Subspace Criterion, is proposed, which makes a small symmetry-breaking change to the Subspace Criterion. Only the true eigenvectors are solutions. Making the corresponding change to the learning rule of the Subspace Network gives a modified learning rule, which can be still implemented on a homogeneous network architecture. In learning, the weight vectors will tend to the true eigenvectors.

This paper presents a destributed algorithm that uses weak copy consistency to create mutual exclusion in a distributed computer system. The weak copy consistency is deduced from the uncertainty of state which occurs due to the finite and unpredictable communication delays in a distributed environment. Also the method correlates outdated state information to current state. The average number of messages to enter critical section in the algorithm is n/2 to n messages where n is the number of sites. We show that the algorithm achieves mutual exclusion and the fairness and liveness of the algorithm is proven. We study the performance of the algorithm by simulation technique.

Lingas developed an NC algorithm for subgraph isomorphism for connected graphs of bounded separator and bounded valence. We present an NC algorithm for computing canonical forms of graphs of bounded separator by using the similar technique.

This paper presents a simple method for avoiding both numerical errors and degeneracy in an incremental-type algorithm for constructing the Voronoi diagram with respect to points on a plane. It is assumed that the coordinates of the given points are represented with a certain fixed number of bits. All the computations in the algorithm are carried out in four times higher precision, so that degeneracy can be discerned precisely. Every time degeneracy is found, the points are perturbed symbolically according to a very simple rule and thus are reduced to a nondegenerate case. The present technique makes a computer program simple in the sense that it avoids all numerical errors and requires no exceptional branches of processing for degenerate cases.

This paper deals with the problem of assigning tasks to the processors of a multiprocessor system such that the sum of execution and communication costs is minimized. If the number of processors is two, this problem can be solved efficiently using the network flow approach pioneered by Stone. This problem is, however, known to be NP-complete in the general case, and thus intractable for systems with a large number of processors. In this paper, we propose a network flow approach for the task assignment problem in homogeneous hypercube networks, i.e., hypercube networks with functionally identical processors. The task assignment problem for an n-dimensional homogeneous hypercube network of N (=2n) processors and M tasks is first transformed into n two-terminal network flow problems, and then solved in time no worse than O(M3 log N) by applying the Goldberg-Tarjan's maximum flow algorithm on each two-terminal network flow problem.

The subject of the paper is to propose a simple O(|V|+|E|) algorithm for finding all 3-edge-components of a given undirected multigraph G=(V, E). An 3-edge-connected component of G is defined as a maximal set of vertices such that G has at least three edge-disjoint paths between every pair of vertices in the set. The algorithm is based on the depth-first search (DFS) technique. For any fixed DFS-tree T of G, cutpairs of G are partitioned into two types: a type 1 pair consists of an edge of T and a back edge; a type 2 pair consists of two edges of T. All type 1 pairs can easily be determined in O(|V|+|E|) time. The point is that an edge set KE(T) in which any type 2 pair is included can be found in O(|V|+|E|) time. All 3-edge-components of G appear as connected components if we delete from G all edges contained in type 1 pairs or in the edge set KE(T).

This paper presents a survey on bicriteria network optimization problems. When there are two conflicting criteria that evaluate the solution, the bicriteria optimization is to find a solution for which these criteria are both acceptably satisfied. Standard approaches to these problems are to combine these two criteria into an aggregated single criterion. Among such problems, this paper first deals with the case in which the aggregated objective function, denoted h(f1(x), f2(x)), is convex in original two objectives f1(x) and f2(x), and, as its special case, it reviews a strongly polynomial algorithm for the bicriteria minimum-cost circulation problem. It then discusses the case in which h is concave and demonstrates that a parametric approach is effective for this case. Several interesting applications in network optimization that belong to this class are also introduced. Finally we deal with the minimum range problems which seek to find a solution such that weights of the components used in the solution are most uniform. We shall present efficient algorithms for solving these problems arised in network optimization.

Suppose that there are terminals on two concentric circles, Cin and Cout, with Cin inside of Cout. We are given a set of nets each of which consists of a terminal on Cin and a terminal on Cout. The routing area is the annular region between the two circles. In this paper, we present an O(nk-1) time algorithm for testing whether the given net set is k-layer routable without vias, where k2 and n is the number of nets.

Suppose that there are terminals on two concentric circles Cin and Cout, with Cin inside of Cout. A set of two-terminal nets is given and the routing area is the annular region between the two circles. In this paper, we present an O(n2) time algorithm for testing whether the given net set is two-layer routable, where n is the number of nets. Applying this algorithm repeatedly, we can find, in O(n3) time, a maximal subset of nets which is two-layer routable.

It is known that the problem of finding a largest common subgraph is NP-hard for general graphs even if the number of input graphs is two. It is also known that the problem can be solved in polynomial time if the input is restricted to two trees. In this paper, a randomized parallel (an RNC) algorithm for finding a largest common subtree of two trees is presented. The dynamic tree contraction technique and the RNC minimum weight perfect matching algorithm are used to obtain the RNC algorithm. Moreover, an efficient NC algorithm is presented in the case where input trees are of bounded vertex degree. It works in O(log(n1)log(n2)) time using O(n1n2) processors on a CREW PRAM, where n1 and n2 denote the numbers of vertices of input trees. It is also proved that the problem is NP-hard if the number of input trees is more than two. The three dimensional matching problem, a well known NP-complete problem, is reduced to the problem of finding a largest common subtree of three trees.

A maximal l-diameter tree cover of a graph G(V,E) is a spanning subgraph C(V,EC) of G such that each connected component of C is a tree, C contains no path with more than l edges, and adding any edge in EEC to C yields either a path of length l1 or a cycle. For every function f from positive integers to positive integers, the maximal f-diameter tree cover prolem (MDTC(f) problem for short) is to find a maximal f(n)-diameter tree cover of G, given an n-node graph G. In this paper, we give two parallel algorithms for the MDTC(f) problem. The first algorithm can be implemented in time O(TMSP(n,f(n))log2n) using polynomial number of processors on an EREW PRAM, where TMSP(n,f(n) is the time needed to find a maximal set of vertex disjoint paths of length f(n) in a given n-node graph using polynomial number of processors on an EREW PRAM. We then show that if suitable restrictions are imposed on the input graph and/or on the magnitude of f, then TMSP(n,f(n))O(logkn) for some constant k and thus, for such cases, we obtain an NC algorithm for the MDTC(f) problem. The second algorithm runs in time O(n log2n/{f(n)1}) using polynomial number of processors on an EREW PRAM. Thus if f(n)Ω(n/logkn) for some kO, we obtain an NC algorithm for the MDTC(f) problem.

Circuit complexity of a Boolean function is defined to be the minimum number of gates in circuits computing the function. In general, the circuit complexity is established by deriving two types of bounds on the complexity. On one hand, an upper bound is derived by showing a circuit, of the size given by the bound, to compute a function. On the other hand, a lower bound is established by proving that a function can not be computed by any circuit of the size. There has been much success in obtaining good upper bounds, while in spite of much efforts few progress has been made toward establishing strong lower bounds. In this paper, after surveying general results concerning circuit complexity for Boolean functions, we explain recent results about lower bounds, focusing on the method of approximation.

A chordal ring network is a processor network on which n processors are arranged to a ring with additional chords. We study a distributed leader election algorithm on chordal ring networks and present trade-offs between the message complexity and the number of chords at each processor and between the message complexity and the length of chords as follows:For every d(1dlog* n1) there exists a chordal ring network with d chords at each processor on which the message complexity for leader election is O(n(log(d1)nlog* n)).For every d(1dlog* n1) there exists a chordal ring network with log(d1)nd1 chords at each processor on which the message complexity for leader election is O(dn).For every m(2mn/2) there exists a chordal ring network whose chords have at most length m such that the message complexity for leader election is O((n/m)log n).