11919636
Quick-release fair scheduling
In prior work on multiprocessor fairness, efficient techniques with provable properties for reallocating spare processing capacity have been elusive. In this paper, we address this shortcoming by proposing a new notion of multiprocessor fairness, called quick-release fair (QRfair) scheduling. Under QRfair scheduling, each task is specified by giving both a minimum and a maximum weight (i.e., processor share). The goal is to schedule each task (as the spare capacity changes) at a rate that is (i) at least that implied by its minimum weight and (ii) at most that implied by its maximum weight. We present a quick-release variant of the PD/sup 2/ Pfair scheduling algorithm called PD/sup Q/ and prove that the allocations of PD/sup Q/ always satisfy (i) and (ii). Also, we present results from simulation experiments that show the efficacy of PD/sup Q/.
5149437
The case for fair multiprocessor scheduling
In this paper, we compare the PD/sup 2/ Pfair algorithm to the EDF-FF partitioning scheme, which uses "first fit" (FF) as a partitioning heuristic and the earliest-deadline-first (EDF) algorithm for per-processor scheduling. We present experimental results that show that PD/sup 2/ is competitive with, and in some cases outperforms, EDF-FF. These results suggest that Pfair scheduling is a viable alternative to partitioning. Furthermore, as discussed herein, Pfair scheduling provides many additional benefits, such as simple and efficient synchronization, temporal isolation, fault tolerance, and support for dynamic tasks.
5519685
Efficient scheduling of soft real-time applications on multiprocessors
In this paper, we consider fair scheduling of soft real-time applications on multiprocessors using the earliest pseudo deadline first (EPDF) Pfair algorithm. Our main contributions are twofold. First, we establish a condition for ensuring a tardiness of at most one quantum under EPDF. This condition is very liberal and should often hold in practice. Second, we present simulation results involving randomly-generated task sets, including those that do not satisfy our condition. In these experiments, deadline misses were rare, and no misses by more than one quantum ever occurred.
18673248
Mixed Pfair/ERfair scheduling of asynchronous periodic tasks
Pfair scheduling was proposed by Baruah, Cohen, Plaxton, and Varvel as a non-work-conserving way of optimally and efficiently scheduling periodic tasks on a multiprocessor. In this paper, we introduce a work-conserving variant of Pfair scheduling called "early-release" fair (ERfair) scheduling. We also present a new scheduling algorithm called PD2 and show that it is optimal for scheduling any mix of early-release and non-early-release asynchronous, periodic tasks. In contrast, almost all prior work on Pfair scheduling has been limited to synchronous systems. PD2 is an optimization of an earlier deadline-based algorithm of Baruah, Gehrke, and Plaxton called PD; PD2 uses a simpler tie-breaking scheme than PD to dis ambiguate equal deadlines. We present a series of counterexamples that suggest that, in general, the PD2 tie-breaking mechanism cannot be simplified. In contrast to this, we show that no tie-breaking information is needed on two-processor systems.
14106112
Mixed Pfair/ERfair scheduling of asynchronous periodic tasks
In this paper, we prove that a simplified variant of the PD Pfair algorithm, called PD/sup 2/, is optimal for scheduling any mix of early-release and non-early-release asynchronous tasks on a multiprocessor. This result breaks new ground by incorporating both early-release and non-early-release tasks under a common framework. In addition, all prior work on optimal multiprocessor Pfair scheduling algorithms has been limited to synchronous periodic task systems.
37206769
Finding Large Independent Sets in Graphs and Hypergraphs
A basic problem in graphs and hypergraphs is that of finding a large independent set---one of guaranteed size. Understanding the parallel complexity of this and related independent set problems on hypergraphs is a fundamental open issue in parallel computation. Caro and Tuza [J. Graph Theory, 15 (1991), pp. 99--107] have shown a certain lower bound $\alpha_k(H)$ on the size of a maximum independent set in a given k-uniform hypergraph H and have also presented an efficient sequential algorithm to find an independent set of size $\alpha_k(H)$. They also show that $\alpha_k(H)$ is the size of the maximum independent set for various hypergraph families. Here, we show that an RNC algorithm due to Beame and Luby [in Proceedings of the ACM--SIAM Symposium on Discrete Algorithms, 1990, pp. 212--218] finds an independent set of expected size $\alpha_k(H)$ and also derandomizes it for certain special cases. (An intriguing conjecture of Beame and Luby implies that understanding this algorithm better may yield an RNC...
12078642
Retrieval scheduling for collaborative multimedia presentations
Abstract. The single-system approach is no longer sufficient to handle the load on popular Internet servers, especially for those offering extensive multimedia content. Such services have to be replicated to enhance their availability, performance, and reliability. In a highly replicated and available environment, server selection is an important issue. In this paper, we propose an application-layer broker (ALB) for this purpose. ALB employs a content-based, client-centric approach to negotiate with the servers and to identify the best server for the requested objects. ALB aims to maximize client buffer utilization in order to efficiently handle dynamic user interactions such as skip, reverse presentation, go back in time. We also present details of a collaborative multimedia presentation platform that we have developed based on ALB.
5246711
Dependent rounding in bipartite graphs
We combine the pipage rounding technique of Ageev & Sviridenko with a recent rounding method developed by Srinivasan (2001), to develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to the following applications: richer random-graph models for graphs with a given degree-sequence; improved approximation algorithms for: (i) throughput-maximization in broadcast scheduling, (ii) delay-minimization in broadcast scheduling, and (iii) capacitated vertex cover; fair scheduling of jobs on unrelated parallel machines. A useful feature of our method is that it lets us prove certain (probabilistic) per-user fairness properties.
6768945
Approximating hyper-rectangles: learning and pseudo-random sets
The PAC learning of rectangles has been studied because they have been found experimentally to yield excellent hypotheses for severaf applied learning problems. Also, pseudorandom sets for rectangles have been actively studied recently because (i) they are a subpmblem common to the derandomization of depth-2 (DIW) circuits and derandotnizing Randomized Logspace, and (ii) they approximate the distribution of n independent multivalued random variables. We present improved upper bounds for a class of such problems of “approximating” highdlmensional rectangles that arise in PAC learning and pseudorandomness.
11619174
Provable algorithms for parallel sweep scheduling on unstructured meshes
We present provably efficient parallel algorithms for sweep scheduling on unstructured meshes. Sweep scheduling is a commonly used technique in radiation transport problems, and involves inverting an operator by iteratively sweeping across a mesh. Each sweep involves solving the operator locally at each cell. However, each direction induces a partial order in which this computation can proceed. On a distributed computing system, the goal is to schedule the computation, so that the length of the schedule is minimized. Several heuristics have been proposed for this problem; but none of the heuristics have worst case performance guarantees. We present a simple, almost linear time randomized algorithm which (provably) gives a schedule of length at most O(log/sup 2/n) times the optimal schedule for instances with n cells, when the communication cost is not considered, and a slight variant, which coupled with a much more careful analysis, gives a schedule of (expected) length O(logmlogloglogm) times the optimal schedule for m processors. These are the first such provable guarantees for this problem. We also design a priority based list schedule using these ideas, with the same theoretical guarantee, but much better performance in practice. We complement our theoretical results with extensive empirical analysis. The results show that (i) our algorithm performs very well and has significantly better performance guarantee in practice and (ii) the algorithm compares favorably with other natural and efficient parallel algorithms proposed in the literature [S. Pautz, (2002), S. Plimpton et al., (2001)].