THE TIME COMPLEXITY OF SCHEDULING INTERVAL ORDERS WITH COMMUNICATION IS POLYNOMIAL

1993 ◽  
Vol 03 (01) ◽  
pp. 53-58 ◽  
Author(s):  
HESHAM H. ALI ◽  
HESHAM EL-REWINI
Keyword(s):  
Execution Time ◽  
Time Complexity ◽  
Linear Time ◽  
Communication Cost ◽  
Interval Order ◽  
Task Graph ◽  
Scheduling Problem ◽  
Interval Orders ◽  
Schedule Length ◽  
Np Complete

Papadimitrjou and Yannakakis showed that unit execution time tasks in interval orders can be scheduled in linear time on N processors when communication cost is ignored. The objective function was to minimize the schedule length. They have also shown that the generalization of this problem to arbitrary execution times is NP- complete . In this paper, we study the problem of scheduling task graphs with communication on N processors when the task graph is an interval order. We prove that this scheduling problem can be solved in polynomial time when the execution cost of the system tasks is identical and equal to the communication cost between any pair of processors. We introduce an algorithm of O(Ne) to minimize the schedule length, where e is the number of arcs in the interval order.

scholarly journals Low complexity algorithms in knot theory

2019 ◽  
Vol 29 (02) ◽  
pp. 245-262
Author(s):  
Olga Kharlampovich ◽  
Alina Vdovina
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Linear Time ◽  
Circuit Complexity ◽  
Equivalence Problem ◽  
Low Complexity ◽  
Combinatorial Structure ◽  
Complexity Classes ◽  
Np Complete ◽  
Almost All

Agol, Haas and Thurston showed that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. This shows that (unless P[Formula: see text]NP) the genus problem has high computational complexity even for knots in a 3-manifold. We initiate the study of classes of knots where the genus problem and even the equivalence problem have very low computational complexity. We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace[Formula: see text]. Alternating knots with some additional combinatorial structure will be referred to as standard. As expected, almost all alternating knots of a given genus are standard. We show that the genus problem for these knots belongs to [Formula: see text] circuit complexity class. We also show, that the equivalence problem for such knots with [Formula: see text] crossings has time complexity [Formula: see text] and is in Logspace[Formula: see text] and [Formula: see text] complexity classes.

scholarly journals Optimal Cooking Procedure Presentation System for Multiple Recipes and Investigating Its Effect

Algorithms ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 67
Author(s):  
Jin Nakabe ◽  
Teruhiro Mizumoto ◽  
Hirohiko Suwa ◽  
Keiichi Yasumoto
Keyword(s):  
Task Scheduling ◽  
Execution Time ◽  
Cooking Time ◽  
Sequential Optimization ◽  
Task Graph ◽  
Scheduling Problem ◽  
Cooking Skill ◽  
The Difference ◽  
Increasing Demand ◽  
Reduce Execution Time

As the number of users who cook their own food increases, there is increasing demand for an optimal cooking procedure for multiple dishes, but the optimal cooking procedure varies from user to user due to the difference of each user’s cooking skill and environment. In this paper, we propose a system of presenting optimal cooking procedures that enables parallel cooking of multiple recipes. We formulate the problem of deciding optimal cooking procedures as a task scheduling problem by creating a task graph for each recipe. To reduce execution time, we propose two extensions to the preprocessing and bounding operation of PDF/IHS, a sequential optimization algorithm for the task scheduling problem, each taking into account the cooking characteristics. We confirmed that the proposed algorithm can reduce execution time by up to 44% compared to the base PDF/IHS, and increase execution time by about 900 times even when the number of required searches increases by 10,000 times. In addition, through the experiment with three recipes for 10 participants each, it was confirmed that by following the optimal cooking procedure for a certain menu, the actual cooking time was reduced by up to 13 min (14.8% of the time when users cooked freely) compared to the time when users cooked freely.

scholarly journals An ILP Formulation for the Task Graph Scheduling Problem Tailored to Bi-Dimensional Reconfigurable Architectures

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
F. Redaelli ◽  
M. D. Santambrogio ◽  
S. Ogrenci Memik
Keyword(s):  
Task Scheduling ◽  
Optimal Schedule ◽  
Reconfigurable Architecture ◽  
Reconfigurable Architectures ◽  
Task Graph ◽  
Scheduling Problem ◽  
Physical Constraints ◽  
Schedule Length ◽  
Extended Analysis ◽  
Task Graph Scheduling

This work proposes an exact ILP formulation for the task scheduling problem on a 2D dynamically and partially reconfigurable architecture. Our approach takes physical constraints of the target device that is relevant for reconfiguration into account. Specifically, we consider the limited number of reconfigurators, which are used to reconfigure the device. This work also proposes a reconfiguration-aware heuristic scheduler, which exploitsconfiguration prefetching, module reuse, andantifragmentationtechniques. We experimented with a system employing two reconfigurators. This work also extends the ILP formulation for a HW/SW Codesign scenario. A heuristic scheduler for this extension has been developed too. These systems can be easily implemented using standard FPGAs. Our approach is able to improve the schedule quality by 8.76% on average (22.22% in the best case). Furthermore, our heuristic scheduler obtains the optimal schedule length in 60% of the considered cases. Our extended analysis demonstrated that HW/SW codesign can indeed lead to significantly better results. Our experiments show that by using our proposed HW/SW codesign method, the schedule length of applications can be reduced by a factor of 2 in the best case.

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

Preemptive Scheduling for Two-Processor Systems

1988 ◽  
Vol 11 (1) ◽  
pp. 1-19
Author(s):  
Andrzej Rowicki
Keyword(s):  
Execution Time ◽  
Preemptive Scheduling ◽  
Total Execution Time ◽  
Schedule Length ◽  
Execution Times ◽  
Dependent Tasks

The purpose of the paper is to consider an algorithm for preemptive scheduling for two-processor systems with identical processors. Computations submitted to the systems are composed of dependent tasks with arbitrary execution times and contain no loops and have only one output. We assume that preemptions times are completely unconstrained, and preemptions consume no time. Moreover, the algorithm determines the total execution time of the computation. It has been proved that this algorithm is optimal, that is, the total execution time of the computation (schedule length) is minimized.

scholarly journals AN EXACT SOLUTION FOR THE RESOURCE-CONSTRAINED CONSTRUCTION SCHEDULING PROBLEM

2016 ◽  
Vol 8 (2) ◽  
pp. 71-78
Author(s):  
Bartłomiej Sroka ◽  
Elżbieta Radziszewska-Zielina
Keyword(s):  
Execution Time ◽  
Critical Path ◽  
Scheduling Problem ◽  
Resource Constrained ◽  
Building Projects ◽  
Construction Scheduling ◽  
Program Sample ◽  
Resource Constrained Scheduling Problem ◽  
The Cost ◽  
Exponential Complexity

Reduced time and, by the same token, the cost of the project is a crucial factor in contemporary construction. This article presents a method for the exact optimisation of a resource-constrained scheduling problem. Based on the Critical Path Method, graph theory and linear programming, an algorithm was developed and the FROPT program was written in Matlab to minimise the execution time of the task. By using the newly-created program, sample networks were calculated and the results were compared with results obtained by using the MS Project scheduling program (using approximation algorithm). The execution time obtained by using FROPT were on average 10% shorter than those obtained using MS Project. In selected cases the improvement in execution time reached 25%. A deterministic approach to the problem may shorten planned project times and bring financial benefits. Due to the exponential complexity of the algorithm, it is most useful in solving small or highly coherent networks. The algorithm and program may result in benefits not offered by commercial software for planners of building projects.

An Area Preserving Transformation Algorithm for Press Forming Blank Development

1993 ◽  
Author(s):  
Nirmal K. Nair ◽  
James H. Oliver
Keyword(s):  
Time Complexity ◽  
Linear Time ◽  
Geometric Interpretation ◽  
Surface Geometry ◽  
Forming Process ◽  
Surface Design ◽  
Design Assessment ◽  
Press Forming ◽  
Blank Shape ◽  
Area Preserving

Abstract An efficient algorithm is presented to determine the blank shape necessary to manufacture a surface by press forming. The technique is independent of material properties and instead uses surface geometry and an area conservation constraint to generate a geometrically feasible blank shape. The algorithm is formulated as an approximate geometric interpretation of the reversal of the forming process. The primary applications for this technique are in preliminary surface design, assessment of manufacturability, and location of binder wrap. Since the algorithm exhibits linear time complexity, it is amenable to implementation as an interactive design aid. The algorithm is applied to two example surfaces and the results are discussed.

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