Ten-Hwang Lai

Mapping pyramid algorithms into hypercubes

Abstract In this paper, we present two algorithms to efficiently embed the pyramid network structure into the hypercube. Each algorithm is analyzed with respect to three specific cost gauges: expansion, dilation, and congestion. Both algorithms maintain optimal expansion and low values for the remaining cost gauges. The first algorithm has congestion two and dilation three; the second has congestion three and dilation two.

Termination detection for dynamically distributed systems with non-first-in-first-out communication

Abstract We propose a new algorithm for detecting termination of distributed systems. The algorithm works correctly whether the system is static or dynamic, whether the interprocess communication is synchronous or asynchronous, and whether the communication channels are first-in-first-out or not. The algorithm requires, in the worst case, O ( nm ) control messages in all, where n is the number of processes in the system and m is the total number of messages transmitted during the operation of the system. After the system terminates, the algorithm is able to detect the termination using only O ( n ) control messages; it is optimal if the system concerned is static.

Preemptive scheduling of independent jobs on a hypercube

Abstract We consider the problem of scheduling n independent jobs on an m-dimensional hypercube system to minimize the finishing time, where each job Ji is associated with a dimension di and a processing time ti, meaning that Ji requires a di-dimensional subcube for ti units of time. An O(n2) algorithm is presented that decides if all n jobs can be finished by a given deadline T. Using this algorithm, one may obtain a minimum-finishing-time schedule in polynomial time.

A compatible and scalable clock synchronization protocol in IEEE 802.11 ad hoc networks

This paper studies the scalability and compatibility problems of clock synchronization in IEEE 802.11 ad hoc networks. The scalability problem of 802.11 timing synchronization has been recognized and studied by researchers in the field, but the proposed solutions are not meeting industry expectation. The compatibility issue is not well investigated by the research community yet. The compatibility issue is very important and practical because of the large deployment base of 802.11 networks. In this paper, we try to address both issues. We propose a simple, compatible protocol without any change of beacon format. The frequency adjustment is proved to be bounded and the maximum clock offset is controlled under 20 /spl mu/s. It is a significant improvement over the current results in the field. The current solutions with similar complexity can only control the maximum clock offset around 125 /spl mu/s for compatible solutions and 50 /spl mu/s for non-compatible protocols.

Message-efficient in-network location management in a multi-sink wireless sensor network

A wireless sensor network consists of many tiny sensor nodes. The distributed memory spaces of sensors can be considered as a large distributed database, in which one can conduct in-network data processing. This paper considers a sensor network used for object tracking where distributed location updates and queries are performed inside the network. Although this issue has been intensively studied for cellular networks, the same problem in sensor networks has very different characteristics. In this paper, we propose an efficient location management scheme for object tracking in a multi-sink sensor network where users can inquire the locations of objects via any sink in the network. A message-efficient algorithm that describes how to perform location updates and queries is proposed. Furthermore, two distributed virtual tree construction algorithms are also presented. The goal is to reduce the overall update and query cost. The efficiency of the proposed algorithms is evaluated and verified by simulations

Scheduling independent jobs on partitionable hypercubes

We consider the problem of scheduling k independent jobs on an n-dimensional hypercube system to minimize finishing time, where each job Ji is associated with a dimension di and a processing time ti, meaning that Ji requires a di-dimensional subcube for ti units of time. This problem is NP-hard if no preemption is allowed. We propose a simple heuristic called LDLPT (largest dimension longest processing time) and analyze its worst-case performance; the ratio of the heuristic to the optimal finishing time does not exceed 2 − 12n−1.

Scheduling Independent Jobs on Hypercubes

We consider the problem of scheduling k independent jobs on an n-dimensional hypercube system to minimize finishing time, where each job J i is associated with a dimension d i and a processing time t i , meaning that J i requires a d i -dimensional subcube for t i units of time. This problem is NP-complete if no preemption is allowed. We propose a simple heuristic called LDLPT (largest dimension largest processing time) for this problem and analyze its worst-case performance: the ratio of the heuristic finishing time to the optimal does not exceed 2 — 1/2n-1.

Exploiting spatial correlation at the link layer for event-driven sensor networks

Wireless Sensor Networks (WSNs) can generally be classified into two categories: time-driven and event-driven. In an event-driven WSN, sensors report their readings only when they detect events. In such behaviour, sensors in the event area may suffer from higher contention. In this paper, we solve this problem by jointly considering two sub-issues. One is exploiting the spatial correlation of sensor data and the other is designing a specific MAC protocol. We propose a novel hybrid TDMA/CSMA protocol with the following interesting features that differentiate itself from traditional TDMA-based protocols: (1) the TDMA part is based on very loose time synchronisation and is triggered by the appearance of events; (2) the slot assignment strategy associated with the TDMA part takes the spatial correlation of sensor data into consideration and thus allows less strict slot allocation than conventional TDMA schemes. Simulation results show the efficiency of the proposed protocol.

On the Embedding of a Class of Regular Graphs in a Faulty Hypercube

In a hypercube of high dimension, the interconnection is quite complex and thus links are likely to fail. In this paper, a general, systematic solution is proposed for the embedding of a group of regular graphs in an injured hypercube with faulty links. These graphs include rings, linear paths, binomial trees, binary trees, meshes, tori, products of the above graphs, and many others. Unlike many existing algorithms which are capable of embedding only one type of graphs, our algorithm embeds the above graphs in a unified way, all centered around a notion callededge matrix.

Ring Embedding in an Injured Hypercube

We consider the problem of embedding a ring in a hypercube that contains possible faulty nodes. Existing algorithms allow the number of faulty nodes to be at most 2n-\Theta(\sqrt {nlogn}), where n is the dimension of the hypercube. We propose an embedding scheme that can tolerate up to \Theta(2^{n/2}) faulty nodes, largely increasing the number of tolerable faulty nodes in a ring embedding.