45060983
Deadline-based scheduling of periodic task systems on multiprocessors
We consider the problem of scheduling periodic task systems on multiprocessors and present a deadline-based scheduling algorithm for solving this problem. We show that our algorithm successfully schedules on m processors any periodic task system with utilization at most m2/(2m - 1).
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.
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.
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.
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.
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.
14399319
Improved distributed algorithms for coloring and network decomposition problems
This paper deals with the problems of computing a maximal independent set and a vertex coloring in a dktributed model of computation. Given a connected graph G = (V, E) with IVI = n and maximum degree A such that G is neither a complete graph nor an odd cycle, Brooks’ theorem shows that G can be colored with A colors. We generalize thk as follows: let G – w be A-colored; then, v can be colored by considering the vertices in an O(loga n) radius around v, and this is tight. Using this, we show that A-coloring G is reducible in 0(log3 n/log A) time to (A+ I)-vertex coloring G in a distributed model. This leads to fast distributed algorithms, and a linear–processor NC algorithm, for Acoloring. We also prove a tight Q(diameter(G)) lower bound for A-edge-coloring bipartite graphs, even with unlimited randomness. When A = 2, this implies an Q(n) lower bound for vertex coloring paths and even cycles. A fundamental notion in distributed graph algorithms is that of a cluster decomposition, introduced by Awerbuch, Goldberg, Luby and Plotkin. We improve the existing bounds by showing how to compute a cluster decomposition in O(n”(’(”)) ) time, where e(n) = 1/=. This implies improved bounds for several problems, such as computing a maximal independent set and a (A + I )-coloring. We also show how to compute a A–coloring within the same time bound, using our reduction technique. Next, we show that the problem of doing better than O(n”(’(m))) time for cluster decomposition is self-reducible to graphs of “intermediate” diameter and degree. This pinpoints the weak points of existing cluster decomposition algorithms. *This research was supported in part by NSF PYI award CGR89-96272 with matching support from UPS and Sun Microsystems. Permission to copy without fee ell or part of this material is granted provided that the copiss are not made or distributed for direct commercial advantage, the ACM copyright notica and tha title of the publication and its date appear, and notice ie given that copying is by permission of the Association for Computing Machinery. To copy otharwise, or to republish, requires a fee and/or specific permieaion. 24th ANNUAL ACM STOC 5/92/VICTORIA, B. C., CANADA a 1992 ACM 0-89791-51 2-7192 /000410!581 . ..$1.50
38425944
Scheduling on Unrelated Machines Under Tree-Like Precedence Constraints
We present polylogarithmic approximations for the R|prec|Cmax and R|prec|∑jwjCj problems, when the precedence constraints are “treelike” – i.e., when the undirected graph underlying the precedences is a forest. We also obtain improved bounds for the weighted completion time and flow time for the case of chains with restricted assignment – this generalizes the job shop problem to these objective functions. We use the same lower bound of “congestion+dilation”, as in other job shop scheduling approaches. The first step in our algorithm for the R|prec|Cmax problem with treelike precedences involves using the algorithm of Lenstra, Shmoys and Tardos to obtain a processor assignment with the congestion + dilation value within a constant factor of the optimal. We then show how to generalize the random delays technique of Leighton, Maggs and Rao to the case of trees. For the weighted completion time, we show a certain type of reduction to the makespan problem, which dovetails well with the lower bound we employ for the makespan problem. For the special case of chains, we show a dependent rounding technique which leads to improved bounds on the weighted completion time and new bicriteria bounds for the flow time.
887266
Approximation Algorithms for Channel Allocation Problems in Broadcast Networks
We study two packing problems that arise in the area of dissemination-based information systems; a second theme is the study of distributed approximation algorithms. The problems considered have the property that the space occupied by a collection of objects together could be significantly less than the sum of the sizes of the individual objects. In the Channel Allocation Problem, there are users who request subsets of items. There are a fixed number of channels that can carry an arbitrary amount of information. Each user must get all of the requested items from one channel, i.e., all the data items of each request must be broadcast on some channel. The load on any channel is the number of items that are broadcast on that channel; the objective is to minimize the maximum load on any channel. We present approximation algorithms for this problem and also show that the problem is MAX-SNP hard. The second problem is the Edge Partitioning Problem addressed by Goldschmidt, Hochbaum, Levin, and Olinick (Networks, 41:13-23, 2003). Each channel here can deliver information to at most k users, and we aim to minimize the total load on all channels. We present an O(n 1/3 )-approximation algorithm and also show that the algorithm can be made fully distributed with the same approximation guarantee; we also generalize to the case of hypergraphs.
38086428
Approximation algorithms for partial covering problems
We study a generalization of covering problems called 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-partial set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-partial 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-partial vertex cover) in polynomial time. Without making any assumption about the number of sets an element is in, 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-partial 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-partial vertex cover on planar graphs, and for covering k points in Rd by disks.