The Buffer Minimization Problem for Multiprocessor Scheduling with Conflicts

Chrobák, Marek; Csirik, János; Imreh, Csanád; Noga, John; Sgall, Jiřį́; Woeginger, Gerhard J.

doi:10.1007/3-540-48224-5_70

Cited by 27 publications

(19 citation statements)

References 7 publications

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“…Bar-Noy et al [7] suggested a different algorithm that simulates the greedy algorithm in the continuous model and is also Θ(log m)-competitive. Chrobak et al [9] studied the more general problem of minimizing the length of the longest queue in a continuous model where queues can be emptied subject to conflict constraints.…”

Section: Side Resultsmentioning

confidence: 99%

Maximizing throughput in multi-queue switches

Azar

Litichevskey

2006

Algorithmica

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We study a basic problem in Multi-Queue switches. A switch connects m input ports to a single output port. Each input port is equipped with an incoming FIFO queue with bounded capacity B. A switch serves its input queues by transmitting packets arriving at these queues, one packet per time unit. Since the arrival rate can be higher than the transmission rate and each queue has limited capacity, packet loss may occur as a result of insufficient queue space. The goal is to maximize the number of transmitted packets. This general scenario models most current networks (e.g., IP networks) which only support a "best effort" service in which all packet streams are treated equally. A 2-competitive algorithm for this problem was designed in [5] for arbitrary B. Recently, a 17 9 ≈ 1.89-competitive algorithm was presented for B > 1 in [3]. Our main result in this paper shows that for B which is not too small our algorithm can do better than 1.89, and approach a competitive ratio of e e−1 ≈ 1.58.

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Section: Side Resultsmentioning

confidence: 99%

Maximizing throughput in multi-queue switches

Azar

Litichevskey

2006

Algorithmica

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“…In particular, they showed how to use cup emptying to produce "fair" job schedules. Chrobak et al [7] introduced a generalization of cup emptying and applied it to multiprocessor scheduling with conflicts between tasks; there is subsequent work by, e.g., Bar-Noy et al [3], Koga [18], and Rote [23]. In the problem, the player can empty more than one cup at a time, but there is a conflict graph between cups.…”

Section: Background and Related Workmentioning

confidence: 99%

The minimum backlog problem

Bender

Fekete

Kröller

et al. 2015

Theoretical Computer Science

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We study the minimum backlog problem (MBP). This online problem arises, e.g., in the context of sensor networks. We focus on two main variants of MBP.The discrete MBP is a 2-person game played on a graph G = (V, E). The player is initially located at a vertex of the graph. In each time step, the adversary pours a total of one unit of water into cups that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player's objective is to minimize the backlog, i.e., the maximum amount of water in any cup at any time.The geometric MBP is a continuous-time version of the MBP: the cups are points in the two-dimensional plane, the adversary pours water continuously at a constant rate, and the player moves in the plane with unit speed. Again, the player's objective is to minimize the backlog.We show that the competitive ratio of any algorithm for the MBP has a lower bound of Ω(D), where D is the diameter of the graph (for the discrete MBP) or the diameter of the point set (for the geometric MBP). Therefore we focus on determining a strategy for the player that guarantees a uniform upper bound on the absolute value of the backlog.For the absolute value of the backlog there is a trivial lower bound of Ω(D), and the deamortization analysis of Dietz and Sleator gives an upper bound of O(D log N ) for N cups. Our main result is a tight upper bound for the geometric MBP: we show that there is a strategy for the player that guarantees a backlog of O(D), independently of the number of cups.We also study a localized version of the discrete MBP: the adversary has a location within the graph and must act locally (filling cups) with respect to his position, just as the player acts locally (emptying cups) with respect to her position. We prove that deciding the value of this game is PSPACE-hard.

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“…From state (1, 1) it is not possible to communicate on b because only T 1 is ready to communicate, not T 2 (T 2 is also connected to b). Also at state (1, 1), T 1 can terminate by taking the transition τ 1 and moving to (3,1).…”

Section: An Examplementioning

confidence: 99%

“…Chrobak et al [1] schedule tasks in a multiprocessor environment to minimize maximum buffer size. Our algorithm does not add scheduling constraints to the problem: it reduces the total buffer size without affecting the schedule, and thereby not affecting the overall speed.…”

Section: Related Workmentioning

confidence: 99%