On optimal message vector length for block single parallel partition algorithm in a three-dimensional ADI solver

It has long been recognized that many direct parallel tridiagonal solvers are only efficient for solving a single tridiagonal equation of large sizes, and they become inefficient when naively used in a three-dimensional ADI solver. In order to improve the parallel efficiency of an ADI solver using a direct parallel solver, we implement the single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication costs. The measured performances show that the longest allowable message vector length (MVL) is not necessarily the best choice. To understand this observation and optimize the performance, we propose an improved model that takes the cache effect into consideration. The optimal MVL for achieving the best performance is shown to depend on number of processors and grid sizes. Similar dependence of the optimal MVL is also found for the popular block pipelined method.     

Path delays in communication networks

A communication network is modelled by a weighted graph. The vertices of the graph represent stations with storage capabilities, while the edges of the graph represent communication channels (or other information processing media). Channel capacity weights are assigned to the edges of the network. The network is assumed to operate in a store-and-forward manner, so that when a channel is busy the messages directed into it are stored at the station, joining there a queue which is governed by a first-come first-served service discipline. Assuming messages, with fixed length, to arrive at random at the network, following the statistics of a Poisson point process, we calculate the statistical characteristics of the message time-delays along a path in a communication network. We solve for the steadystate distributions of the message waiting-times along the path, for the distribution of the overall message delay-time, for the average memory size requirements at the stations, as well as for other statistical characteristics of the message flow and the queueing processes along a communication path.     

A combinatorial algorithm for the TDMA message scheduling problem

In this paper, we introduce a combinatorial algorithm for the message scheduling problem on Time Division Multiple Access (TDMA) networks. In TDMA networks, time is divided in to slots in which messages are scheduled. The frame length is defined as the total number of slots required for all stations to broadcast without message collisions. The objective is to provide a broadcast schedule of minimum frame length which also provides the maximum throughput. This problem is known to be -hard, thus efficient heuristics are needed to provide solutions to real-world instances. We present a two-phase algorithm which exploits the combinatorial structure of the problem in order to provide high quality solutions. The first phase finds a feasible frame length in which the throughput is maximized in phase two. Computational results are provided and compared with other heuristics in the literature as well as to the optimal solutions found using a commercial integer programming solver. Experiments on 63 benchmark instances show that the proposed method is able to provide optimal frame lengths for all cases with near optimal throughput.     

A heuristic file reorganization algorithm based on record clustering

The problem of file organization which we consider involves altering the placement of records on pages of a secondary storage device. In addition, we want this reorganization to be done in-place, i.e., using the file's original storage space for the newly reorganized file. The motivation for such a physical change is to improve the database system's performance. For example, by placing frequently and jointly accessed records on the same page or pages, we can try to minimize the number of page accesses made in answering a set of queeries. The optimal assignment (or reassignment) of records to clusters is exactly what record clustering algorithms attempt to do. However, record clustering algorithms usually do not solve the entire problem, i.e., they do not specify how to efficiently reorganize the file to reflect the clustering assignment which they determine. Our algorithm is a companion to general record clustering algorithms since it actually transforms the file. The problem of optimal file reorganization isNP-hard. Consequently, our reorganization algorithm is based on heuristics. The algorithm's time and space requirements are reasonable and its solution is near optimal. In addition, the reorganization problem which we consider in this paper is similar to the problem of join processing when indexes are used.The research of this author was partially supported by the National Science Foundation under grant IST-8696157.     

移位交换网的最优路由算法

移位交换网是重要的互联网络之一 ,在并行计算中有着广泛应用 .然而 ,它缺少任意点对间的最短路由算法 .已有的路由算法都不能保证其任意节点对间都是最短路由 .文中给出了一个最短路由算法 ,也是最优路由算法 ,它使得从源节点到目的节点的任何信息都是沿最短路由传输 .同时 ,我们还得到了任意节点对间的距离公式     

On queueing delays of dispersed messages

We study the message queueing delays in a node of a communication system, where a message consists of a block of consecutive packets. The message delay is defined as the time elapsing between the arrival epoch of the first packet of the message to the system until after the transmission of the last packet of that message is completed. We distinguish between two types of message generation processes. The message can be generated as abatch or it can bedispersed over time. In this paper we focus on the dispersed generation model. The main difficulty in the analysis is due to the correlation between the system states observed by different packets of the same message. This paper introduces a new technique to analyze the message delay in such systems for different arrival models and different number of sessions. For anM/M/1 system with variable size messages and for the bursty traffic model, we obtain an explicit expression for the Laplace-Stieltjes transform (LST) of the message delay. Derivations are also provided for anM/G/1 system, for multiple session systems and for fixed message sizes. We show that the correlation has a strong effect on the performance of the system, and that the commonly usedindependence assumption, i.e., the assumption that the delays of packets are independent from packet to packet, can lead to wrong conclusions.     

Optimal gathering protocols on paths under interference constraints

We study the problem of gathering information from the nodes of a multi-hop radio network into a predefined destination node under reachability and interference constraints. In such a network, a node is able to send messages to other nodes within reception distance, but doing so it might create interference with other communications. Thus, a message can only be properly received if the receiver is reachable from the sender and there is no interference from another message being transmitted simultaneously. The network is modeled as a graph, where the vertices represent the nodes of the network and the edges, the possible communications. The interference constraint is modeled by a fixed integer d≥1, which implies that nodes within distance d in the graph from one sender cannot receive messages from another node. In this paper, we suppose that each node has one unit-length message to transmit and, furthermore, we suppose that it takes one unit of time (slot) to transmit a unit-length message and during such a slot we can have only calls which do not interfere (called compatible calls). A set of compatible calls is referred to as a round. We give protocols and lower bounds on the minimum number of rounds for the gathering problem when the network is a path and the destination node is either at one end or at the center of the path. These protocols are shown to be optimal for any d in the first case, and for 1≤d≤4, in the second case.     

Conditional targeting for communication

In this work we propose the use of a targeting method applied to chaotic systems in order to reach special trajectories that encode arbitrary sources of messages. One advantage of this procedure is to overcome dynamical constraints which impose limits in the amount of information that the chaotic trajectories can encode. Another advantage is the message decoding, practically instantaneous and independent of any special technique or algorithm. Furthermore, with this procedure, information can be transmitted with no errors due to bounded noise.     

Asymptotic optimality of the static frequency caching in the presence of correlated requests

It is well known that the static caching algorithm that keeps the most frequently requested documents in the cache is optimal in case when documents are of the same size and requests are independent and identically distributed. However, it is hard to develop explicit and provably optimal caching algorithms when requests are statistically correlated. In this paper, we show that keeping the most frequently requested documents in the cache is still optimal for large cache sizes even if the requests are strongly correlated.     

Records in the classical and quantum standard map

Record statistics is the study of how new highs or lows are created and sustained in any dynamical process. The study of the highest or lowest records constitute the study of extreme values. This paper represents an exploration of record statistics for certain aspects of the classical and quantum standard map. For instance the momentum square or energy records is shown to behave like that of records in random walks when the classical standard map is in a regime of hard chaos. However different power laws is observed for the mixed phase space regimes. The presence of accelerator modes are well-known to create anomalous diffusion and we notice here that the record statistics is very sensitive to their presence. We also discuss records in random vectors and use it to analyze the quantum standard map via records in their eigenfunction intensities, reviewing some recent results along the way.     

Choquet integral for record linkage

Record linkage is used in data privacy to evaluate the disclosure risk of protected data. It models potential attacks, where an intruder attempts to link records from the protected data to the original data. In this paper we introduce a novel distance based record linkage, which uses the Choquet integral to compute the distance between records. We use a fuzzy measure to weight each subset of variables from each record. This allows us to improve standard record linkage and provide insightful information about the re-identification risk of each variable and their interaction. To do that, we use a supervised learning approach which determines the optimal fuzzy measure for the linkage.     

Nonlinear integer programming for optimal allocation in stratified sampling

A stratified random sampling plan is one in which the elements of the population are first divided into nonoverlapping groups, and then a simple random sample is selected from each group. In this paper, we focus on determining the optimal sample size of each group. We show that various versions of this problem can be transformed into a particular nonlinear program with a convex objective function, a single linear constraint, and bounded variables. Two branch and bound algorithms are presented for solving the problem. The first algorithm solves the transformed subproblems in the branch and bound tree using a variable pegging procedure. The second algorithm solves the subproblems by performing a search to identify the optimal Lagrange multiplier of the single constraint. We also present linearization and dynamic programming methods that can be used for solving the stratified sampling problem. Computational testing indicates that the pegging branch and bound algorithm is fastest for some classes of problems, and the linearization method is fastest for other classes of problems.     

Bin packing with divisible item sizes

We study a variety of NP-hard bin packing problems under a divisibility constraint that generalizes the often encountered situation in which all item sizes are powers of 2. For ordinary one-dimensional bin packing, we show that First Fit Decreasing produces optimal packings under this restriction, and that if in addition the largest item size divides the bin capacity, then even the less powerful First Fit algorithm is optimal. Similar results are obtained for two-dimensional bin packing and multiprocessor scheduling, along with several other simple variants. For more complicated problems, like vector packing and dynamic bin packing, the improvement is less substantial, and we indicate why.     

An efficient step size control for continuation methods

In solving a nonlinear equation by the use of a continuation method one of the crucial problems is the choice of the step sizes. We present a model for the total computational cost of a standard numerical continuation process and solve the problem of optimal step size control for this model. Using the theoretical results as a basis, we develop an adaptive step size algorithm for Newton's method. This procedure is computationally inexpensive and it gives quite satisfactory results compared to some other numerical experiments found in the literature.     

Efficient public key encryption with smallest ciphertext expansion from factoring

For public key encryption schemes, adaptive chosen ciphertext security is a widely accepted security notion since it captures a wide range of attacks. SAEP and SAEP+ are asymmetric encryption schemes which were proven to achieve semantic security against adaptive chosen ciphertext attacks. However, the bandwidth for message is essentially worse, that is the ciphertext expansion (the length difference between the ciphertext and the plaintext) is too large. In most of the mobile networks and bandwidth constrained communication systems, it is necessary to securely send as many messages as possible. In this article, we propose two chosen-ciphertext secure asymmetric encryption schemes. The first scheme is a generic asymmetric encryption padding scheme based on trapdoor permutations. The second one is its application to the Rabin-Williams function which has a very fast encryption algorithm. These asymmetric encryption schemes both achieve the optimal bandwidth w.r.t. the ciphertext expansion, namely with the smallest ciphertext expansion. Further, tight security reductions are shown to prove the security of these encryption schemes.     

Portfolio selection under possibilistic mean–variance utility and a SMO algorithm

In this paper, we propose a new portfolio selection model with the maximum utility based on the interval-valued possibilistic mean and possibilistic variance, which is a two-parameter quadratic programming problem. We also present a sequential minimal optimization (SMO) algorithm to obtain the optimal portfolio. The remarkable feature of the algorithm is that it is extremely easy to implement, and it can be extended to any size of portfolio selection problems for finding an exact optimal solution.     

Optimal Batch Sizes for a Two-Stage Production System

A 2-stage production model is considered in which items are processed in batches at both stages. Items processed at Stage 1 are stored until needed at Stage 2 and new batches are processed at Stage 1 only when necessary to meet second stage demand. It is shown that in an optimal policy the batch size at the first stage must be an integer multiple of second stage batch size. This can be used in an analytical derivation of the optimum batch sizes.     

Crane scheduling with non-crossing constraint

In this paper, we examine crane scheduling for ports. This important component of port operations management is studied when the non-crossing spatial constraint, which is common to crane operations, is considered. We assume that ships can be divided into holds and that cranes can move from hold to hold but jobs are not pre-emptive, so that only one crane can work on one hold or job to complete it. Our objective is to minimize the latest completion time for all jobs. We formulate this problem as an integer programming problem. We provide the proof that this problem is NP-complete and design a branch-and-bound algorithm to obtain optimal solutions. A simulated annealing meta-heuristic with effective neighbourhood search is designed to find good solutions in larger size instances. The elaborate experimental results show that the branch-and-bound algorithm runs much faster than CPLEX and the simulated annealing approach can obtain near optimal solutions for instances of various sizes.     

A biased random-key genetic algorithm for the Steiner triple covering problem

We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used to evaluate solution procedures for this problem. The new covers for instances A ₄₀₅ and A ₇₂₉ have sizes 335 and 617, respectively. On all other smaller instances our algorithm consistently produces covers of optimal size.