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.
12321308
Efficient gossip-based aggregate computation
Recently, there has been a growing interest in gossip-based protocols that employ randomized communication to ensure robust information dissemination. In this paper, we present a novel gossip-based scheme using which all the nodes in an n-node overlay network can compute the common aggregates of MIN, MAX, SUM, AVERAGE, and RANK of their values using O(n log log n) messages within O(log n log log n) rounds of communication. To the best of our knowledge, ours is the first result that shows how to compute these aggregates with high probability using only O(n log log n) messages. In contrast, the best known gossip-based algorithm for computing these aggregates requires O(nlog n) messages and O(log n) rounds. Thus, our algorithm allows system designers to trade off a small increase in round complexity with a significant reduction in message complexity. This can lead to dramatically lower network congestion and longer node lifetimes in wireless and sensor networks, where channel bandwidth and battery life are severely constrained.
15971402
Pfair scheduling: beyond periodic task systems
We consider variants of Pfair and ER-fair scheduling in which subtasks may be released late, i.e., there may be separation between consecutive windows of the same task. We call such tasks intra-sporadic tasks. There are two main contributions. First, we show the existence of a Pfair (and hence ER-fair) schedule for any intra-sporadic task system whose utilization is at most the number of available processors. Second, we give a polynomial-time algorithm that is optimal for scheduling intra-sporadic tasks in a Pfair or ER-fair manner on systems of one or two processors.
13618830
Optimal rate-based scheduling on multiprocessors
The PD2 Pfair/ERfair scheduling algorithm is the most efficient known algorithm for optimally scheduling periodic tasks on multiprocessors. In this paper, we prove that PD2 is also optimal for scheduling "rate-based" tasks whose processing steps may be highly jittered. The rate-based task model we consider generalizes the widely-studied sporadic task model.
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.
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)].
5089320
Better approximation guarantees for job-shop scheduling
Job-shop scheduling is a classical NP-hard problem. Shmoys, Stein, and Wein presented the first polynomial-time approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work and present further improvements for some important NP-hard special cases of this problem (e.g., in the preemptive case where machines can suspend work on operations and later resume). We also present NC algorithms with improved approximation guarantees for some NP-hard special cases.
15562468
Low discrepancy sets yield approximate min-wise independent permutation families
Motivated by a problem of filtering near-duplicate Web documents, Broder, Charikar, Frieze and Mitzenmacher defined the following notion of ϵ-approximate min-wise independent permutation families. A multiset F of permutations of {0,1,…,n−1} is such a family if for all K⫅{0,1,…,n−1} and any x∈K, a permutation π chosen uniformly at random from F satisfies 
|Pr[min{π(K)}=π(x)]−1|K||≤ϵ|K|. 
We show connections of such families with low discrepancy sets for geometric rectangles, and give explicit constructions of such families F of size nO(logn) for ϵ=1/nΘ(1), improving upon the previously best-known bound of Indyk. We also present polynomial-size constructions when the min-wise condition is required only for |K|≤2O(log2/3n), with ϵ≥2−O(log2/3n).
42237174
On the Complexity of Distributed Network Decomposition
In this paper, we improve the bounds for computing a network decomposition distributively and deterministically. Our algorithm computes an (n?(n),n?(n))-decomposition innO(?(n))time, whereformula. As a corollary we obtain improved deterministic bounds for distributively computing several graph structures such as maximal independent sets and ?-vertex colorings. We also show that the class of graphs G whose maximum degree isnO(?(n))where ?(n)=1/log lognis complete for the task of computing a near-optimal decomposition, i.e., a (logn, logn)-decomposition, in polylog(n) time. This is a corollary of a more general characterization, which pinpoints the weak points of existing network decomposition algorithms. Completeness is to be intended in the following sense: if we have an algorithmAthat computes a near-optimal decomposition in polylog(n) time for graphs inG, then we can compute a near-optimal decomposition in polylog(n) time for all graphs.
1506015
Approximation Algorithms for Partial Covering Problems
We study the generalization of covering problems to partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example, in k-set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-set cover, if each element occurs in at most f sets, then we derive a primal-dual f-approximation algorithm (thus implying a 2-approximation for k-vertex cover) in polynomial time. In addition to its simplicity, this algorithm has the advantage of being parallelizable. For instances where each set has cardinality at most three, we obtain an approximation of 4/3. We also present better-than-2-approximation algorithms for k-vertex cover on bounded degree graphs, and for vertex cover on expanders of bounded average degree. We obtain a polynomial-time approximation scheme for k-vertex cover on planar graphs, and for covering points in Rd by disks.