Xiaotie Deng

How to learn an unknown environment

The authors consider the problem faced by a newborn that must explore and learn an unknown room with obstacles in it. They seek algorithms that achieve a bounded ratio of the worst-case distance traversed in order to see all visible points of the environment (thus creating a map), divided by the optimum distance needed to verify the map. The situation is complicated by the fact that the latter offline problem (optimally verifying a map) is NP-hard and thus must be solved approximately. Although the authors show that there is no such competitive algorithm for general obstacle courses, they give a competitive algorithm for the case of a polygonal room with a bounded number of obstacles in it.<<ETX>>

Competitive implementation of parallel programs

Abstract. We apply the methodology of competitive analysis of algorithms to the implementation of programs on parallel machines. We consider the problem of finding the best on-line distributed scheduling strategy that executes in parallel an unknown directed acyclic graph (dag) which represents the data dependency relation graph of a parallel program and which is revealed as execution proceeds. We study the competitive ratio of some important classes of dags assuming a fixed communication delay ratio τ that captures the average interprocessor communication measured in instruction cycles. We provide competitive algorithms for divide-and-conquer dags, trees, and general dags, when the number of processors depends on the size of the input dag and when the number of processors is fixed. Our major result is a lower bound Ω (τ/ logτ ) of the competitive ratio for trees; it shows that it is impossible to design compilers that produce almost optimal execution code for all parallel programs. This fundamental result holds for almost any reasonable distributed memory parallel computation model, including the LogP and BSP model.

Competitive Distributed Decision-Making

We study several natural problems in distributed decision-making from the standpoint of competitive analysis; in these problems incomplete information is a result of the distributed nature of the problem, as opposed to the on-line mode of decision making that was heretofore prevalent in this area. In several simple situations of distributed scheduling, the competitive ratio can be computed exactly, and the different ratios can be used as a measure of the value of information and communication between decision-makers. In a more general distributed scheduling situation, we give tight upper and lower bounds on the competitive ratio achievable in the deterministic case, and give an optimal randomized algorithm with a much better competitive ratio.

Preemptive Scheduling of Parallel Jobs on Multiprocessors

We study the problem of processor scheduling for n parallel jobs applying the method of competitive analysis. We prove that for jobs with a single phase of parallelism, a preemptive scheduling algorithm without information about job execution time can achieve a mean completion time within 2 2 n+1 times the optimum. In other words, we prove a competitive ratio of 2 2 n+1 . The result is extended to jobs with multiple phases of parallelism (which can be used to model jobs with sublinear speedup) and to interactive jobs (with phases during which the job has no CPU requirements) to derive solutions guaranteed to be within 4 4 n+1 times the optimum. In comparison with previous work, our assumption that job execution times are unknown prior to their completion is more realistic, our multiphased job model is more general, and our approximation ratio (for jobs with a single phase of parallelism) is tighter and cannot be improved. While this work presents theoretical results obtained using competitive analysis, we believe that the results provide insight into the performance of practical multiprocessor scheduling algorithms that operate in the absence of complete information.

Non-clairvoyant multiprocessor scheduling of jobs with changing execution characteristics (extended abstract)

In this work theoretically proves that Equi-partition eeciently schedules multiprocessor batch jobs with diierent execution characteristics. Motwani et al.show that the mean response time of jobs is within two of optimal for fully parallelizable jobs. We extend this result by considering jobs with multiple phases of arbitrary nondecreasing and sublinear speedup functions. Having no knowledge of the jobs being scheduled (non-clairvoyant) one would not expect it to perform well. However, our main result shows that the mean response time obtained with Equi-partition is no more than 2 + p 3 3:73 times the optimal. The paper also considers schedulers with diierent numbers of preemptions and jobs with more general classes of speedup functions. Matching lower bounds are also proved.

Competitive dynamic multiprocessor allocation for parallel applications

In this paper we use competitive analysis to study preemptive multiprocessor allocation policies for parallel jobs whose execution time is not known to the scheduler at the time of scheduling. The objective is to minimize the makespan (i.e., the completion time of the last job to finish executing). We characterize a parallel job, J/sub i/, by two parameters: its execution time, l/sub i/, and its parallelism, P/sub i/, which may vary over time. The preemption and reallocation of processors can take place at any time. We devise a preemptive policy which achieves the best possible competitive ratio and then derive upper and lower bounds for scheduling N parallel jobs on P processors.

Optimal amortized distributed consensus

Are randomized consensus algorithms more powerful than deterministic ones? Seemingly so, since randomized algorithms exist that reach consensus in expected constant number of rounds, whereas the deterministic counterparts are constrained by the r ≥ t + 1 lower bound in the number of communication rounds, where t is the maximum number of faults to be tolerated.

Good algorithm design style for multiprocessors

We discuss a style of designing parallel algorithms with the following characteristics for a problem of the best known sequential time T(n): C1. Each processor spends O(T(n)/P) time in computing. C2. Each processor sends and/or receives O(n/P) messages of one-word-size. C3. The number of communication phases/sup 1/ is constant, independent of the input size n. We show this is possible to achieve for several fundamental computational problems.<<ETX>>

Competitive Dynamic Multiprocessor Allocation for Parallel Applications

We study dynamic multiprocessor allocation policies for parallel jobs, which allow the preemption and reallocation of processors to take place at any time. The objective is to minimize the completion time of the last job to finish executing (the makespan). We characterize a parallel job using two parameter. The jobs parallelism, Pi, which is the number of tasks being executed in parallel by a job, and its execution time, li, when Pi processors are allocated to the job. The only information available to the scheduler is the parallelism of jobs. The job execution time is not known to the scheduler until the jobs execution is completed. We apply the approach of competitive analysis to compare preemptive scheduling policies, and are interested in determining which policy achieves the best competitive ratio (i.e., is within the smallest constant factor of optimal). We devise an optimal competitive scheduling policy for scheduling two parallel jobs on P processors. Then, we apply the method to schedule N parallel jobs on P processors. Finally we extend our work to incorporate jobs for which the number of parallel tasks changes during execution (i.e., jobs with multiple phases of parallelism).