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### Scheduling Algebra [chapter]

Rob van Glabbeek, Peter Rittgen
<span title="">1998</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Our goal is to develop an algebraic theory of process scheduling. We specify a syntax for denoting processes composed of actions with given durations.  ...  We show that a normal form exists for every term of the algebra and establish both soundness of our axioms with respect to a schedule semantics and completeness for efficient processes.  ...  We call it scheduling algebra and develop its theoretical framework in the following sections. An example process is given in fig. 1 . Its algebraic term is: a; (b || c; d) || e.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-49253-4_21">doi:10.1007/3-540-49253-4_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7pga2lvwjzeuxbvm4nu2nvkcgy">fatcat:7pga2lvwjzeuxbvm4nu2nvkcgy</a> </span>
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### Process algebra, process scheduling, and mutual exclusion [article]

C. A. Middelburg
<span title="2020-04-21">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The choice of ACP_ϵ stems from the need to cover more process-scheduling policies. We show that a process-scheduling policy supporting mutual exclusion of critical subprocesses is now covered.  ...  In the case of multi-threading as found in contemporary programming languages, parallel processes are interleaved according to what is known as a process-scheduling policy in the field of operating systems  ...  Each of the theorems refers to more than one process algebra. It is implicit that the same set A of actions and the same communication function γ are assumed in the process algebras referred to.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2003.00473v3">arXiv:2003.00473v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rvjlyguajnhifoa64mve74ibmi">fatcat:rvjlyguajnhifoa64mve74ibmi</a> </span>
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### An Algebra of Synchronous Scheduling Interfaces

Michael Mendler
<span title="2011-01-22">2011</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
In this paper we propose an algebra of synchronous scheduling interfaces which combines the expressiveness of Boolean algebra for logical and functional behaviour with the min-max-plus arithmetic for quantifying  ...  The resulting algebra of interface types aims to provide a general setting for specifying type-directed and compositional analyses of worst-case scheduling bounds.  ...  They generate a plus-min algebra of scheduling sequences which is not a linear algebra, as it does not satisfy distribution.  ...
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### Algebraic specification of a communication scheduler [chapter]

Mathai Joseph, Abha Moitra
<span title="">1985</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Operationally, this framework is a communication scheduler : formally, it is specified Mgebraically as a data type.  ...  A particular data type can be algebraically described in a number of different ways. It is therefore important to know why a particular algebraic specification is chosen.  ...  ALGEBRAIC SPECIFICATION The algebraic specification of a data type consists of the definition of the set of operations, or functions, of the data type together with axioms which provide the semantics of  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-15199-0_23">doi:10.1007/3-540-15199-0_23</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lfjrl7ugnvbl5ogfoxg6au5z5a">fatcat:lfjrl7ugnvbl5ogfoxg6au5z5a</a> </span>
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### Algebraic solution of tropical optimization problems via matrix sparsification with application to scheduling

Nikolai Krivulin
<span title="">2017</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/75odiq25o5gtzcy4h7mdcztb5y" style="color: black;">Journal of Logical and Algebraic Methods in Programming</a> </i> &nbsp;
We apply the results to solve real-world problems drawn from project (machine) scheduling, and give numerical examples.  ...  Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative  ...  We start with a standard description of the scheduling problem, and then represent it in terms of tropical algebra.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jlamp.2017.03.004">doi:10.1016/j.jlamp.2017.03.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tasyi4wyrnayleasrm3ryhol4e">fatcat:tasyi4wyrnayleasrm3ryhol4e</a> </span>
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### A Linear Algebraic Framework for Quantum Internet Dynamic Scheduling [article]

Paolo Fittipaldi
<span title="2022-05-20">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
To this end, we introduce a novel discrete-time algebraic model for arbitrary network topology, including transmission and memory losses, and adapted to dynamic scheduling decisions.  ...  Our algebraic model allows the scheduler to use the storage of temporary intermediate links to optimize the performance, depending on the information availability, ranging from full global information  ...  SCHEDULING APPLICATION The algebraic framework presented above poses as a tool to gauge the performance and requirements of different scheduling policies.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2205.10000v1">arXiv:2205.10000v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6jpjdsucqrfpjhgrfv3ass6oc4">fatcat:6jpjdsucqrfpjhgrfv3ass6oc4</a> </span>
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### Scheduling Trees of Malleable Tasks for Sparse Linear Algebra [article]

Abdou Guermouche and Loris Marchal and Bertrand Simon and Frédéric Vivien
<span title="2015-06-04">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In such a distributed setting (homogeneous or heterogeneous), we prove the NP-completeness of the corresponding scheduling problem, and propose some approximation algorithms.  ...  We largely simplify their proofs by resorting only to pure scheduling arguments. Building on the insight gained thanks to these new proofs, we extend the study to distributed multicore platforms.  ...  In this paper, we focus on task graphs coming from sparse linear algebra, and especially from the factorization of sparse matrices using the multifrontal method.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1410.7249v2">arXiv:1410.7249v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y6rpihxotngzfavhefauuad6iq">fatcat:y6rpihxotngzfavhefauuad6iq</a> </span>
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### An algebraic approach to project schedule development under precedence constraints [article]

Nikolai Krivulin
<span title="2012-10-24">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
An approach to schedule development in project management is developed within the framework of idempotent algebra.  ...  As a result, many issues in project scheduling reduce to solving computational problems in the idempotent algebra setting, including linear equations and eigenvalue-eigenvector problems.  ...  Furthermore, examples of actual problems in project scheduling are considered. We show how to formulate the problems in terms of idempotent algebra, and present related algebraic solutions.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1210.6508v1">arXiv:1210.6508v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w5atuo4uercorbx6uqw6v3hfty">fatcat:w5atuo4uercorbx6uqw6v3hfty</a> </span>
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### Process-Algebraic Analysis of Timing and Schedulability Properties [chapter]

Anna Philippou, Oleg Sokolsky
<span title="2007-07-23">2007</span> <i title="Chapman and Hall/CRC"> Chapman &amp; Hall/CRC Computer &amp; Information Science Series </i> &nbsp;
This fact plays a significant role in the algebra and it is exploited for performing schedulability analysis.  ...  Schedulability Analysis Within the ACSR formalism we can conduct two types of analysis for real-time scheduling: validation and schedulability analysis.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1201/9781420011746.ch31">doi:10.1201/9781420011746.ch31</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cejb7zjsuzeybgvjwwurlgxrxi">fatcat:cejb7zjsuzeybgvjwwurlgxrxi</a> </span>
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### PARS: A Process Algebra with Resources and Schedulers [chapter]

MohammadReza Mousavi, Michel Reniers, Twan Basten, Michel Chaudron
<span title="">2004</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The goal of this approach is to facilitate and formalize introduction of scheduling concepts into process algebraic specification using separate specifications for resource requiring processes, schedulers  ...  In this paper, we introduce a dense time process algebraic formalism with support for specification of (shared) resource requirements and resource schedulers.  ...  consuming schedulers) can be beneficial.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-40903-8_11">doi:10.1007/978-3-540-40903-8_11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7d3k247sh5euxfuucjwmpz7swa">fatcat:7d3k247sh5euxfuucjwmpz7swa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20040713182427/http://www.ics.ele.tue.nl:80/~tbasten/papers/pars_formats.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4f/a3/4fa3e1a9992fb60601e72a157bcd4b85e02ec32f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-40903-8_11"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### Generalized public transportation scheduling using max-plus algebra

<span title="2018-05-02">2018</span> <i title="Institute of Information Theory and Automation"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wvmwhbjaz5bdrghzzimuwtodnu" style="color: black;">Kybernetika (Praha)</a> </i> &nbsp;
The regular schedule is constructed by using the spectral properties over max-plus algebra.  ...  Some works on the scheduling of some systems using max-plus algebra have been discussed in the literature.  ...  algebra.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.14736/kyb-2018-2-0243">doi:10.14736/kyb-2018-2-0243</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/it7cqakcjrcd3mvqkzepgfia2u">fatcat:it7cqakcjrcd3mvqkzepgfia2u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180723015456/https://dml.cz/bitstream/handle/10338.dmlcz/147192/Kybernetika_54-2018-2_2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/dd/98/dd9834735bd6cfbfcad25e08fcdb9e9032a13363.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.14736/kyb-2018-2-0243"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

### Scheduling dense linear algebra operations on multicore processors

Jakub Kurzak, Hatem Ltaief, Jack Dongarra, Rosa M. Badia
<span title="">2010</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o454xj4tdjfllm3oragfkdrffi" style="color: black;">Concurrency and Computation</a> </i> &nbsp;
SCHEDULING DENSE LINEAR ALGEBRA OPERATIONS 35 Figure 17. Static pipeline implementation of the tile QR factorization.  ...  SCHEDULING DENSE LINEAR ALGEBRA OPERATIONS 17 Cilk Cilk was developed at the MIT Laboratory for Computer Science starting in 1994 [9].  ...  Exper. 2010; 22:15-44 DOI: 10.1002/cpe SCHEDULING DENSE LINEAR ALGEBRA OPERATIONS 19 Concurrency Computat.: Pract.  ...
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150921002345/http://www.netlib.org//utk/people/JackDongarra-20130-07-11/PAPERS/schedule-dense-linear.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c7/db/c7db0caa72a20b6b11ae60dbd768e34cae1fb08c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/cpe.1467"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

### Task scheduling for mobile robots using interval algebra

Lenka Mudrova, Nick Hawes
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nytnrt3gtzbixld5r6a4talbky" style="color: black;">2015 IEEE International Conference on Robotics and Automation (ICRA)</a> </i> &nbsp;
Our contribution is the use of Allen's interval algebra to prune the search to be performed by the mixed integer program. This significantly speeds up the algorithm.  ...  The scheduling problem is formalised as mixed integer program, which is a standard approach in the scheduling community.  ...  The main contribution of our work is the use of Allen's interval algebra to prune possible solutions within the scheduler.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icra.2015.7139027">doi:10.1109/icra.2015.7139027</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icra/MudrovaH15.html">dblp:conf/icra/MudrovaH15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/biaunm35abdcjfumk2nxt5lgba">fatcat:biaunm35abdcjfumk2nxt5lgba</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170312182030/http://www.cs.bham.ac.uk/~nah/bibtex/papers/mudrova_ICRA15.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a1/83/a183b0f688ca76d6f2bb3e3069d29b69e57181f5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icra.2015.7139027"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

### Delay Composition Algebra: A Reduction-Based Schedulability Algebra for Distributed Real-Time Systems

Praveen Jayachandran, Tarek Abdelzaher
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v45oxowmzff5lbub4ixtl2tazu" style="color: black;">2008 Real-Time Systems Symposium</a> </i> &nbsp;
This paper presents the delay composition algebra: a set of simple operators for systematic transformation of distributed real-time task systems into single-resource task systems such that schedulability  ...  The transformation allows performing schedulability analysis on distributed systems using uniprocessor theory and analysis tools.  ...  Introduction In this paper, we present an algebra for schedulability analysis of distributed real-time systems.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/rtss.2008.38">doi:10.1109/rtss.2008.38</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/rtss/JayachandranA08.html">dblp:conf/rtss/JayachandranA08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pgcwxfgccrd2nnrughwgj2b5zi">fatcat:pgcwxfgccrd2nnrughwgj2b5zi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808025712/http://web.engr.illinois.edu/~zaher/cyberphysical/Papers/RTSS08.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3f/1d/3f1db01a133de44c428a278e1150754d34735952.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/rtss.2008.38"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

### Scheduling optimization of parallel linear algebra algorithms using Supervised Learning [article]

G. Laberge and S. Shirzad and P. Diehl and H. Kaiser and S. Prudhomme and A. Lemoine
<span title="2019-09-25">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Blaze's linear algebra library.  ...  However, finding the optimal way to schedule the workload between threads is a non-trivial problem because it depends on the structure of the algorithm being parallelized and the hardware the executable  ...  Some of the dynamic scheduling methods include: Pure Self-scheduling, Chunk Self-scheduling, Guided Self-scheduling [3] , Factoring [4] and Trapezoid Self-scheduling [5, 1] .  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1909.03947v2">arXiv:1909.03947v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6dnzgsegkbf2lhqnzdxlhxkepy">fatcat:6dnzgsegkbf2lhqnzdxlhxkepy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200930070816/https://arxiv.org/pdf/1909.03947v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e8/fe/e8fe020a57dbe273edc4ac747bff72a61406b480.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1909.03947v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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