Primal-Dual Algorithms for Deterministic Inventory Problems

Primal-Dual Algorithms for Deterministic Inventory Problem

Computational complexity

Computational complexity . . . insightintothequestionwhycertaincomputationalproblems appeartobemoredicultthan others.Computationhasaddedadimensiontothestudyof combinatorics.Thetheoremthat, 4.InsideP exists?Althoughsuchanalgorithmisknownforthematchingproblem, thisisnotthecasefor manycombinatorialproblems.Indeed,thegreatestchallenge confrontingcomplexitytheoryisto providetechniquestoprovethatnoecientalgorithmexistsforagivenproblem. path,isnotthecompleteanswer;isitpossibletoecientlyconstructalargermatchingifone referredtothetextbooksbyGarey&Johnson(1979)andHopcroft&Ullman(1979)aswellasto thesequestions,andwhilesubstantialprogresshasbeenmadetowardsdistinguishingthediculty ofcomputationalproblems,mostofthebasicissuesremainunresolved.Inthischapter,wewill describethefundamentalsofthistheoryandgiveabriefsurveyoftheresultsthathavebeen obtainedinitsrstquartercentury.Foramoredetailedandcompleteexposition,thereaderis Computationalcomplexitytheoryprovidesthemathematicalframeworkinwhichtodiscuss themorerecentHandbookofTheoreticalComputerScienceeditedbyvanLeeuwen(1990). 1ComplexityofComputationalProblems computationalproblem,settingupamathematicalmodelofcomputation,andthenformalizing complexityofcomputationalproblems.Thisinvolvesdescribingwhatispreciselymeantbya thenotionofthecomputationalresourcesrequiredforaproblemwithrespecttothatmodel. Unfortunately,thereisnoonestandardizedspecicationinwhichtodiscussthesequestions.For thistheorytoproducemeaningfulresults,itisessentialthatthedenitionsberobustenoughsotha

Improved approximation algorithms for shop scheduling problems

This paper published in Proceedings of the International Congress of Mathematicians, Kyoto, Japan (1990), 1595-160

Permutation vs. non-permutation flow shop schedules

This paper published in Proceedings Sixth Annual ACM Symposium on Computational Geometry, Berkeley, CA (1990), 63-7

Two Level Job-Scheduling Strategies for a Computational Grid

Abstract. We address parallel jobs scheduling problem for computa-tional GRID systems. We concentrate on two-level hierarchy scheduling: at the first level broker allocates computational jobs to parallel comput-ers. At the second level each computer generates schedules of the par-allel jobs assigned to it by its own local scheduler. Selection, allocation strategies, and efficiency of proposed hierarchical scheduling algorithms are discussed.

Improved approximation algorithms for network design problems

Improved approximation algorithms for network design problem