An On-Line Scheduling Heuristic with Better Worst-Case Ratio Than Graham’s List Scheduling

1993 ◽  
Vol 22 (2) ◽  
pp. 349-355 ◽  
Author(s):  
Gábor Galambos ◽  
Gerhard J. Woeginger
Keyword(s):  
List Scheduling ◽  
Worst Case ◽  
Worst Case Ratio ◽  
On Line ◽  
Scheduling Heuristic

A Note on "An On-Line Scheduling Heuristic with Better Worst Case Ratio than Graham's List Scheduling"

1997 ◽  
Vol 26 (3) ◽  
pp. 870-872 ◽  
Author(s):  
R. Chandrasekaran ◽  
Bo Chen ◽  
Gábor Galambos ◽  
P. R. Narayanan ◽  
André Van Vliet ◽  
...  
Keyword(s):  
List Scheduling ◽  
Worst Case ◽  
Worst Case Ratio ◽  
On Line ◽  
Scheduling Heuristic

scholarly journals On-line ranking of split graphs

2013 ◽  
Vol Vol. 15 no. 2 (Graph and Algorithms) ◽  
Author(s):  
Piotr Borowiecki ◽  
Dariusz Dereniowski
Keyword(s):  
Clique Number ◽  
Ranking Algorithm ◽  
Worst Case ◽  
Split Graph ◽  
Worst Case Ratio ◽  
Vertex Ranking ◽  
International Audience ◽  
On Line ◽  
Split Graphs ◽  
Positive Integers

Graphs and Algorithms International audience A vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm and the number of colors used in an optimal off-line solution may be arbitrarily large. This negative result motivates us to investigate semi on-line algorithms, where a split graph is presented on-line but its clique number is given in advance. We prove that there does not exist a (2-ɛ)-competitive semi on-line algorithm of this type. Finally, a 2-competitive semi on-line algorithm is given.

Scheduling Mixed-Criticality Real-Time Tasks in a Fault-Tolerant System

2015 ◽  
Vol 6 (2) ◽  
pp. 65-86 ◽  
Author(s):  
Jian (Denny) Lin ◽  
Albert M. K. Cheng ◽  
Doug Steel ◽  
Michael Yu-Chi Wu ◽  
Nanfei Sun
Keyword(s):  
Real Time ◽  
Fault Tolerant ◽  
Formal Proof ◽  
Worst Case ◽  
Real Time Scheduling ◽  
Important Trend ◽  
Time Scheduling ◽  
On Line ◽  
Computer Tasks ◽  
Mixed Criticality

Enabling computer tasks with different levels of criticality running on a common hardware platform has been an increasingly important trend in the design of real-time and embedded systems. On such systems, a real-time task may exhibit different WCETs (Worst Case Execution Times) in different criticality modes. It is well-known that traditional real-time scheduling methods are not applicable to ensure the timely requirement of the mixed-criticality tasks. In this paper, the authors study a problem of scheduling real-time, mixed-criticality tasks with fault tolerance. An optimal, off-line algorithm is designed to guarantee the most tasks completing successfully when the system runs into the high-criticality mode. A formal proof of the optimality is given. Also, a novel on-line slack-reclaiming algorithm is proposed to recover from computing faults before the tasks' deadline during the run-time. Simulations show that an improvement of about 30% in performance is obtained by using the slack-reclaiming method.

ON-LINE SUPPLY VOLTAGE SCALING BASED ON IN SITU DELAY MONITORING TO ADAPT FOR PVTA VARIATIONS

2012 ◽  
Vol 21 (08) ◽  
pp. 1240027 ◽  
Author(s):  
MARTIN WIRNSHOFER ◽  
NASIM POUR ARYAN ◽  
LEONHARD HEISS ◽  
DORIS SCHMITT-LANDSIEDEL ◽  
GEORG GEORGAKOS
Keyword(s):  
Closed Loop ◽  
Supply Voltage ◽  
Average Power ◽  
Voltage Scaling ◽  
Error Rates ◽  
Design Flow ◽  
Chain Model ◽  
Worst Case ◽  
On Line

The presented Pre-Error Adaptive Voltage Scaling (AVS) approach tunes the supply voltage of digital circuits dependent on the present Process, Voltage and Temperature variations as well as Aging (PVTA). By exploiting unused timing margin, produced by state-of-the-art worst-case designs, power consumption is minimized. Timing information of the circuit is obtained by in situ delay monitors (Pre-Error flip-flops), detecting late-arriving signals (pre-errors) in critical paths. Based on the occurrence of pre-errors, the voltage is adjusted by a low-overhead control unit connected to the on-chip voltage regulator. As the voltage is adapted during normal circuit operation (on-line), the randomness of the applied input pattern has to be considered. We developed a Markov chain model, based on transistor level simulations, to describe the resulting statistics of the closed-loop voltage control. With this model, the risk of overcritical voltage reductions and the effect of global and local variations on the closed-loop control can be analyzed. For an arithmetic circuit, synthesized in an industrial 65nm design-flow, an average power saving of 23% (including all overheads) is achieved for very low error rates below 1E-11.

scholarly journals Parallel Machine Scheduling with Batch Delivery to Two Customers

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Xueling Zhong ◽  
Dakui Jiang
Keyword(s):  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Variable Cost ◽  
Worst Case ◽  
Batch Delivery ◽  
Worst Case Ratio ◽  
Processing Facility ◽  
Production And Distribution ◽  
Distribution Cost

In some make-to-order supply chains, the manufacturer needs to process and deliver products for customers at different locations. To coordinate production and distribution operations at the detailed scheduling level, we study a parallel machine scheduling model with batch delivery to two customers by vehicle routing method. In this model, the supply chain consists of a processing facility withmparallel machines and two customers. A set of jobs containingn1jobs from customer 1 andn2jobs from customer 2 are first processed in the processing facility and then delivered to the customers directly without intermediate inventory. The problem is to find a joint schedule of production and distribution such that the tradeoff between maximum arrival time of the jobs and total distribution cost is minimized. The distribution cost of a delivery shipment consists of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment. We provide polynomial time heuristics with worst-case performance analysis for the problem. Ifm=2and(n1-b)(n2-b)<0, we propose a heuristic with worst-case ratio bound of 3/2, wherebis the capacity of the delivery shipment. Otherwise, the worst-case ratio bound of the heuristic we propose is2-2/(m+1).

SCHEDULING FILE TRANSFERS UNDER PORT AND CHANNEL CONSTRAINTS

1993 ◽  
Vol 04 (02) ◽  
pp. 101-115 ◽  
Author(s):  
SHIN-ICHI NAKANO ◽  
TAKAO NISHIZEKI
Keyword(s):  
Communication Channel ◽  
Edge Coloring ◽  
Large Collection ◽  
File Transfer ◽  
Worst Case ◽  
File Transfers ◽  
Worst Case Ratio ◽  
Efficient Approximation Algorithm ◽  
New Type ◽  
Efficient Approximation

The file transfer scheduling problem was introduced and studied by Coffman, Garey, Johnson and LaPaugh. The problem is to schedule transfers of a large collection of files between various nodes of a network under port constraint so as to minimize the overall finishing time. This paper extends their model to include communication channel constraint in addition to port constraint. We formulate the problem with both port and channel constraints as a new type of edge-coloring of multigraphs, called an fg-edge-coloring, and give an efficient approximation algorithm with absolute worst-case ratio 3/2.

scholarly journals Optimal Computer Crash Performance Precaution

2012 ◽  
Vol Vol. 14 no. 1 (Distributed Computing and...) ◽  
Author(s):  
Efraim Laksman ◽  
Hakan Lennerstad ◽  
Lars Lundberg
Keyword(s):  
Completion Time ◽  
Optimal Allocation ◽  
Parallel Program ◽  
Parallel Computer ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Worst Case Ratio ◽  
International Audience ◽  
Computer Crash ◽  
The Cost

Distributed Computing and Networking International audience For a parallel computer system with m identical computers, we study optimal performance precaution for one possible computer crash. We want to calculate the cost of crash precaution in the case of no crash. We thus define a tolerance level r meaning that we only tolerate that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use optimal allocation on m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then, what is the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time of the same parallel program? We denote the maximal ratio of completion times f(r, m) - i.e., the ratio for worst-case programs. In the paper we establish upper and lower bounds of the worst-case cost function f (r, m) and characterize worst-case programs.

scholarly journals On the Comparison Complexity of the String Prefix-Matching Problem

1995 ◽  
Vol 2 (46) ◽  
Author(s):  
Dany Breslauer ◽  
Livio Colussi ◽  
Laura Toniolo
Keyword(s):  
Linear Time ◽  
String Matching ◽  
Random Access ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Matching Problem ◽  
Machine Model ◽  
Worst Case ◽  
On Line ◽  
Sequential Comparison

In this paper we study the exact comparison complexity of the string<br />prefix-matching problem in the deterministic sequential comparison model<br />with equality tests. We derive almost tight lower and upper bounds on<br />the number of symbol comparisons required in the worst case by on-line<br />prefix-matching algorithms for any fixed pattern and variable text. Unlike<br />previous results on the comparison complexity of string-matching and<br />prefix-matching algorithms, our bounds are almost tight for any particular pattern.<br />We also consider the special case where the pattern and the text are the<br />same string. This problem, which we call the string self-prefix problem, is<br />similar to the pattern preprocessing step of the Knuth-Morris-Pratt string-matching<br />algorithm that is used in several comparison efficient string-matching<br />and prefix-matching algorithms, including in our new algorithm.<br />We obtain roughly tight lower and upper bounds on the number of symbol<br />comparisons required in the worst case by on-line self-prefix algorithms.<br />Our algorithms can be implemented in linear time and space in the<br />standard uniform-cost random-access-machine model.

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