Parallel O(log(n)) time edge-colouring of trees and Halin graphs

We present parallel O(log(n))-time algorithms for optimal edge colouring of trees and Halin graphs with n processors on a a parallel random access machine without write conflicts (P-RAM). In the case of Halin graphs with a maximum degree of three, the colouring algorithm automatically finds every Hamiltonian cycle of the graph

The effect of dietary taurine and its potential biosynthesis on juvenile grey mullet (Mugil cephalus) performance

The grey mullet is a catadromous species that spawns in the taurine-rich seawater environment, followed by the young fish generally migrating to less saline, low taurine waters during the larva-juvenile transition. Consequently, this study aimed to (1) determines whether there is a dietary taurine requirement in juvenile grey mullet for enhanced growth and (2) the potential for taurine biosynthesis. The experimental system consisted of sixteen 400-l V-tanks, where filtered, UV-treated ambient seawater (40 ‰) entered the bottom of the tanks at a rate of 7 tank exchanges/day. This allowed the testing of four 1 mm pelleted diets (0, 0.5, 1.0, and 2.0% taurine DW diet) in replicates of 4 tanks/treatment for 58 days. Grey mullet juveniles demonstrated (P<0.05) a specific requirement for a 0.5% taurine DW diet for improved growth. Fish fed the taurine diets displayed populations with a markedly (P < 0.05) higher average number of surviving fish (23.4±1.1) of moderately sized (10- 20 g) cohorts than smaller (< 10 g) individuals (12.5±1.1). In contrast, the fish fed the taurine control (0% taurine) exhibited similar average numbers of small and moderate sized fish (18.0±3.6-20.0±4.1). Dietary taurine accumulated highly (P<0.05) in the muscles in a dose dependent manner but less so (P<0.05) in eyes, and liver. The gene expression of liver cysteine sulfinic acid decarboxylase (CSD) exhibited an upregulation (P<0.05) with taurine diets from 0 to 1% but was down regulated (P<0.05) in fish fed the 2% taurine DW diet

Time and space optimal implementations of atomic multi-writer register

AbstractThis paper addresses the wide gap in space complexity of atomic, multi-writer, multi-reader register implementations. While the space complexity of all previous implementations is linear, the lower bounds are logarithmic. We present three implementations which close this gap: The first implementation is sequential and its role is to present the idea and data structures used in the second and third implementations. The second and third implementations are both concurrent, the second uses multi-reader physical registers while the third uses single-reader physical registers. Both the second and third implementations are optimal with respect to the two most important complexity criteria: Their space complexity is logarithmic and their time complexity is linear

Uniform Self-Stabilizing Leader Election Part 2: General Graph Protocol

A distributed system is self-stabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The self-stabilization property makes the system tolerant to faults in which processors crash and then recover spontaneously in an arbitrary state. When the intermediate period in between one recovery and the next crash is long enough, the system stabilizes. A distributed system is uniform if all processors with the same number of neighbors are identical. A distributed system is dynamic if it can tolerate addition or deletion of processors and links without reinitialization. In this work, we study uniform dynamic self-stabilizing protocols for leader election under read/write atomicity. Our protocols use randomization to break symmetry. We first introduce self-stabilizing protocols for synchronization. Then, usin

Resource bounds for self stabilizing message driven protocols

Abstract. Self-stabilizing message driven protocols are defined and discussed. The class weakexclusion that contains many natural tasks such as ℓ-exclusion and token-passing is defined, and it is shown that in any execution of any self-stabilizing protocol for a task in this class, the configuration size must grow at least in a logarithmic rate. This last lower bound is valid even if the system is supported by a time-out mechanism that prevents communication deadlocks. Then we present three self-stabilizing message driven protocols for token-passing. The rate of growth of configuration size for all three protocols matches the aforementioned lower bound. Our protocols are presented for two processor systems but can be easily adapted to rings of arbitrary size. Our results have an interesting interpretation in terms of automata theory

On the complexity of sequential rectangle placement in ieee 802.16/wimax systems

We study the problem of scheduling transmissions on the Downlink of IEEE 802.16/WiMAX systems that use the OFDMA technology. These transmissions are scheduled using a matrix whose dimensions are frequency and time, where every matrix cell is a time slot on some carrier channel. The IEEE 802.16 standard mandates that (i) every transmission occupies a rectangular set of cells, and (ii) transmissions must be scheduled according to a given order. We show that if the number of cells required by a transmission is not limited (up to the matrix size), the problem of maximizing matrix utilization is very hard to approximate. On the positive side we show that if the number of cells of every transmission is limited to some constant fraction of the matrix area, the problem can be approximated to within a constant factor. As far as we know this is the first paper that considers this sequential rectangle placement problem