Properties of optimal hop-by-hop allocation policies in networkswith multiple transmitters and linear equal holding costs

Flow control between one receiving node and its adjacent transmitting nodes in a computer network is modeled as a Markov decision problem. By deriving several qualitative properties of an optimal allocation policy, it is shown that finding dynamic optimal allocations for only T states suffices to completely describe an optimal allocation policy. When the number of transmitters M=2, for all but one of the T states there are only two allocations that are candidates for optimality. It is desirable to extend this property to M>2. However, it appears that the technique used for M =2 does not generalize to M>2     

Simple algorithms and architectures for B-spline interpolation

It is proved that the Toeplitz binary value matrix inversion associated with mth-order B-spline interpolation can be implemented using only 2(m+1) additions. Pipelined architectures are developed for real-time B-spline interpolation based on simple running average filters. It is shown that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can be implemented using B-splines with M+2 multiplies. With insignificant loss of performance, the coefficients at the knots of the truncated sinc function can be approximated using coefficients which are powers of two. The resulting implementation requires only M+4m+6 additions. It is believed that the truncated sinc function approximated by zero-order B-spline functions actually achieves the best visual performance     

Optimal flow control allocation policies in communication networkswith multiple message classes

Flow control is considered for M(⩾2) transmitting stations sending packets to a single receiver over a slotted time-multiplexed link. The optimal allocation problem is generalized to the case of nonidentical holding costs at the M transmitters. Qualitative properties of optimal discounted and time-average policies that reduce the computational complexity of the M-dimensional optimal flow control algorithm are derived. For M=2, a simple relationship between optimal allocations for states x and x +e_i (i=1,2) that leads to significant computational savings in the optimal algorithm is established     

Optimal control of premature queueing

Given an M/G/1 queue, a special customer, and an exponential random variable M that is independent of the queueing process, if the special customer reaches the front of the queue before the time specified by M, it cannot be processed and must re-enter the queue at the back. While waiting in the queue, the available decisions for the special customer are either to keep its position in the queue or to leave its position to join the back of the queue. The author's goal is to find a strategy that minimizes the expected delay until the special customer starts being processed. The move-along policy is to always stay in the queue until the front of the queue is reached, and if it cannot be served, to join the back of the queue. The basic result is that if the queue is stable, the move-along policy is optimal     

Odd even shifts in SIMD hypercubes

A linear-time algorithm is developed to perform all odd (even) length circular shifts of data in an SIMD (single-instruction-stream, multiple-data-stream) hypercube. As an application, the algorithm is used to obtain an O(M²+log N) time and O(1) memory per processor algorithm to compute the two-dimensional convolution of an N×N image and an M×M template on an N² processor SIMD hypercube. This improves the previous best complexity of O(M² log M+log N)     

Convolution on mesh connected multicomputers

An efficient parallel algorithm is presented for convolution on a mesh-connected computer with wraparound. The algorithm does not require a broadcast feature for data values, as assumed by previously proposed algorithms. As a result, the algorithm is applicable to both SIMD and MIMD meshes. For an N×N image and a M×M template, the previous algorithms take O (M²q) time on an N×N mesh-connected multicomputer (q is the number of bits in each entry of the convolution matrix). The algorithms have complexity O(M²r), where r=max {number of bits in an image entry, number of bits in a template entry}. In addition to not requiring a broadcast capability, these algorithms are faster for binary images     

A distributed M-ary hypothesis testing problem withcorrelated observations

The distributed M-ary hypothesis testing problem of detecting one of M₀ events by an (N+1)-person hierarchical team, when the observations are correlated, is examined. In this problem, each of the N subordinate decision makers (DMs) transmits one of a prespecified set of messages based on their data to a primary decision maker who, in turn, combines the messages with his or her own data to make the final team decision. The necessary conditions for the optimal decision rules of the DMs are derived. A nonlinear Gauss-Seidel iterative algorithm is developed for the person-by-person optimal decision rules, and its monotonic convergence to the person-by-person optimum is established. A fast approximation algorithm is proposed for computing certain conditional probabilities arising in the person-by-person optimal decision rules. The algorithms are illustrated with several examples, and implications for distributed organizational designs are pointed out     

A new realization theory

A realization theory that is based on the Kalman system theory and motivated by the Fuhrmann realization theory is presented. In the Fuhrmann realization theory, the realization state-space is defined by a natural polynomial module K_Q, which is related to a nonsingular polynomial matrix Q. The module K_Q is formed of all f where Q^-1f is strictly proper. In the realization theory proposed, the realization state-space is defined by a different module M_Q, which is formed of properly truncated, strictly proper formal power series of Q^-1f. The realization theory can be used to prove the dual-realization scheme induced by the Fuhrmann realization theory     

Fast in-place verification of data dependencies

Several fast and space-optimal sequential and parallel algorithms for solving the satisfaction problem of functional and multivalued dependencies (FDs and MVDs) are presented. Two frameworks to verify an MVD for a relation and their implementation by exploring the existing fast space-optimal sorting techniques are described. The space optimality means that only a constant amount of extra memory space is needed for the sequential implementations, and O(M) amount of extra memory space for parallel algorithms that use M processors. This feature makes the algorithms attractive whenever space is a critical resource and I/O transfers should be reduced to the minimal, as is often the case for relational database systems. The time requirements for in-place FD and MVD verification are given in terms of M and of N, which is the number of tuples in a relation. The effect of relation modification on FD and MVD verification is examined     

Job scheduling in a partitionable mesh using a two-dimensionalbuddy system partitioning scheme

The job scheduling problem in a partitionable mesh-connected system in which jobs require square meshes and the system is a square mesh whose size is a power of two is discussed. A heuristic algorithm of time complexity O(n(log n+log p)), in which n is the number of jobs to be scheduled and p is the size of the system is presented. The algorithm adopts the largest-job-first scheduling policy and uses a two-dimensional buddy system as the system partitioning scheme. It is shown that, in the worst case, the algorithm produces a schedule four times longer than an optimal schedule, and, on the average, schedules generated by the algorithm are twice as long as optimal schedules     

Some new properties of the structured singular value

J.C. Doyle et al. (1982) have shown that a necessary and sufficient condition for robust stability or robust performance in the H^∞-frame work may be formulated as a bound on the structured singular value (μ) of a specific matrix M which includes information on the system model, the controller, the model uncertainty, and the performance specifications. Often it is desirable to express the robust stability and performance conditions as norm bounds on transfer matrices (T) which are of direct interest to the engineer, e.g. sensitivity or complementary sensitivity. The present paper shows how to derive bounds on σ(T) from bounds on μ(M)     

Clustering on a hypercube multicomputer

Squared error clustering algorithms for single-instruction multiple-data (SIMD) hypercubes are presented. The algorithms are shown to be asymptotically faster than previously known algorithms and require less memory per processing element (PE). For a clustering problem with N patterns, M features per pattern, and K clusters, the algorithms complete in O(k+log NM ) steps on NM processor hypercubes. This is optimal up to a constant factor. These results are extended to the case in which NMK processors are available. Experimental results from a multiple-instruction, multiple-data (MIMD) medium-grain hypercube are also presented     

M-dimensional Cayley-Hamilton theorem

The theorem states that every block square matrix satisfies its own m-D (m-dimensional, m⩾1) matrix characteristic polynomial. The exact statement and a simple proof of this theorem are given. The theorem refers to a matrix A subdivided into m blocks, and hence having dimension at least m. The conclusion is that every square matrix A with dimension M satisfies several m-D characteristic matrix polynomials with degrees N₁ . . ., N _m, such that N₁+ . . . +N_m ⩽M     

What's in a set of points? [straight line fitting]

The problem of fitting a straight line to a planar set of points is reconsidered. A parameter space computational approach capable of fitting one or more lines to a set of points is presented. The suggested algorithm handles errors in both coordinates of the data points, even when the error variances vary between coordinates and among points and can be readily made robust to outliers. The algorithm is quite general and allows line fitting according to several useful optimality criteria to be performed within a single computational framework. It is observed that certain extensions of the Hough transform can be turned to be equivalent to well-known M estimators, thus allowing computationally efficient approximate M estimation     

A generalized relational model for indefinite and maybe information

A generalized relational model which is capable of representing and manipulating disjunctive and maybe kinds of information is presented. A data structure, called M-table, is defined, and the information contained in the M-table is precisely stated. Redundant information in M-tables is characterized, and an operator to remove this redundant information is presented. The relational algebra is suitably generalized to deal with M-tables. Additional operators, R-projection and merge, are presented. Queries can be expressed as a combination of the various generalized relational algebraic operators. The M-table accurately models the two bounds on the external interpretation of a query. The sure component of an M-table corresponds to one of the bounds which is the set of objects which belong to the external interpretation of the query. The maybe component of an M-table corresponds to the other bound which is the set of objects for which the possibility of belonging to the external interpretation of the query cannot be ruled out     

Tree searched chain coding for subpixel reconstruction of planarcurves

Coding schemes for the quantization of line drawings that outperform basic chain codes are investigated. First, subpixel accuracy reconstruction is obtained by a simple linear filtering of the chain code points, which achieves a factor-of-three to-four reduction in average reconstruction distortion for smooth curves. Second, the basic chain encoding schemes are generalized to a multipath-tree-searched encoding scheme. A variation of the (M,L)-algorithm is used to maintain M contending chain code paths in storage and choose the best path from these. Over a wide variety of source curves, tree-searched chain coding results in nearly an order of magnitude reduction in average reconstruction distortion over smoother chain codes. The performance improvement for curves is obtained with only a slight increase in bit rate over basic chain codes     

The design of a precompensator for multivariable adaptive control-anetwork-theoretic approach

A network-theoretic approach to the design of a dynamic precompensator C(s) for a multiinput, multioutput plant T(s) is considered. The design is based on the relative degree of each element of T(s). Specifically, an efficient algorithm is presented for determining whether a given plant T(s) has a diagonal precompensator C( s) such that, for almost all cases, T(s)C (s) has a diagonal interactor. The algorithm also finds any optimal precompensator, in the sense that the total relative degree is minimal. The algorithm can be easily modified to work even when a T(s) represented by a nonsquare matrix is given     

Limited lookahead policies in supervisory control of discrete eventsystems

A supervisory control scheme which is based on limited lookahead control policies is proposed, using an online scheme where after the occurrence of an event, the next control action is determined on the basis of an N-step-ahead projection of the behavior of the process (represented as an N-level tree). This procedure then repeats after the execution of the next event. Different attitudes can be adopted to calculate a control action for the given N-level tree in order to resolve uncertainties about the process behavior beyond N steps. Two such attitudes, termed conservative and optimistic. are studied. Results are presented pertaining to monotonicity and convergence properties of the optimistic and conservative N-step policies in terms of N, and comparison of these policies with the optimal offline solution; closed-form expression for the language generated by the N-step conservative policy for prefix-closed legal languages; and lower bounds for N that guarantee that the online scheme performs as well as an offline scheme with complete information     

Optimal parallel initialization algorithms for a class of priorityqueues

An adaptive parallel algorithm for inducing a priority queue structure on an n-element array is presented. The algorithm is extended to provide optimal parallel construction algorithms for three other heap-like structures useful in implementing double-ended priority queues, namely min-max heaps, deeps, and min-max-pair heaps. It is shown that an n-element array can be made into a heap, a deap, a min-max heap, or a min-max-pair heap in O(log n+(n /p)) time using no more than n/log n processors, in the exclusive-read-exclusive-write parallel random-access machine model