Theoretical Aspects of Computer Science

This book presents the revised final versions of eight lectures given by leading researchers at the First Summer School on Theoretical Aspects of Computer Science in Tehran, Iran, in July 2000. The lectures presented are devoted to quantum computation, approximation algorithms, self-testing/correction, algebraic modeling of data, the regularity lemma, multiple access communication and combinatorial designs, graph-theoretical methods in computer vision, and low-density parity-check codes.

TheFirstSummerSchoolonTheoreticalAspectsonComputerSciencewasheld attheInstituteforStudiesinTheoreticalPhysicsandMathematics(IPM)from July3-10,2000. Theideaoforganizingasummerschoolwasoriginatedduringaconversation betweenthe?rstandthesecondeditorofthisvolumeinthewinterof2000at IPMinTehran. ThedecisionwasformalizedwhenthethirdeditorvisitedIPM laterinthewinter. ThemainideabehindtheSummerSchoolwastointroducetothestudents in Iran some of the highly innovative and promising research in Theoretical ComputerScience,and,atthesametime,tostarta?owofideasbetweentop researchersinthe?eldandtheIranianscientists. Forthisreason,thetalkswere designedtobeofatutorialstyle. Theorganizersdecidedtoconcentrateonafewimportantareasofresearch in modern Theoretical Computer Science. To attract students to this imp- tant area, they also decided to include talks on applications of methods from TheoreticalComputerSciencetootherareas. ThisvolumecontainsthewrittencontributionstotheprogramofthisS- mer School. It is intended for students and researchers who want to gain - quaintancewithcertaintopicsinTheoreticalComputerScience. Thepaperson quantumcomputation,approximationalgorithms,self-testing/correcting,al- braic modeling of data, and the Regularity Lemma correspond to the former category,whileconnectionsbetweenmultipleaccesscommunicationandcom- natorialdesigns,graph-theoreticalmethodsincomputervision,andlow-density parity-checkcodesbelongtothelattercategory. Eachcontributiontothisvolumewaspresentedinatwohoursession,l- vingampletimeforquestionsanddiscussions. Thetutorialswerefollowedbya numberofspecializedtalkstouchingoncurrentresearchproblemsinthearea. Partsofthetalkshavebeenincorporatedintothematerialofthecontributions. January2002 G. B. Khosrovshahi A. Shokoufandeh A. Shokrollahi Organization The ?rst International Summer School on Theoretical Aspects of Computer Science was organized by the Institute for Studies in Theoretical Physics and Mathematics(IPM)inTehran,Iran. ProgramCommittee ConferenceChair: G. B. Khosrovshahi,IPMandtheUniversity ofTehran,Iran A. Shokoufandeh,DrexelUniversity,USA A. Shokrollahi,DigitalFountain,USA Local Arrangements: M. Zamani SponsoringInstitutions SchoolofMathematics,Institutefor Studies in Theoretical Physics and Mathematics(IPM),Tehran,Iran World Mathematical Year (WMY) 2000 National Commission Service de Coop eration et d Action Culturelle,AmbassadedeFranceen Iran Neda Rayaneh Institute (NRI) neda. net. ir VIII Acknowledgements WearegratefultoProfessorM. J. Larijani,thedirectorofIPM,whohasbeen a great advocate for the expansion of Theoretical Computer Science at the - stitute,andhelpedussecuremajorfundingfromIPM. Wewouldalsoliketo expressourthankstoProfessorS. Shahshahani,theDeputyDirectorofIPM, who was most helpful in soliciting ?nancial support from the World Mathe- tical Year 2000 National Commission. The Service de Coop eration et d Action Culturelle of the French embassy in Iran kindly provided travel funds for our invited speakers from France. We thank the Service Culturelle for their generous support. Finally,wewouldliketoexpressourgratitudetoM.

Includes supplementary material: sn.pub/extras

Klappentext

The ?rst International Summer School on Theoretical Aspects of Computer Science was organized by the Institute for Studies in Theoretical Physics and Mathematics(IPM)inTehran,Iran. ProgramCommittee ConferenceChair: G. B. Khosrovshahi,IPMandtheUniversity ofTehran,Iran A. Shokoufandeh,DrexelUniversity,USA A. Shokrollahi,DigitalFountain,USA Local Arrangements: M. Zamani SponsoringInstitutions SchoolofMathematics,Institutefor Studies in Theoretical Physics and Mathematics(IPM),Tehran,Iran World Mathematical Year (WMY) 2000 National Commission Service de Coop eration et d Action Culturelle,AmbassadedeFranceen Iran Neda Rayaneh Institute (NRI) http://www. neda. net. ir VIII Acknowledgements WearegratefultoProfessorM. J. Larijani,thedirectorofIPM,whohasbeen a great advocate for the expansion of Theoretical Computer Science at the - stitute,andhelpedussecuremajorfundingfromIPM. Wewouldalsoliketo expressourthankstoProfessorS. Shahshahani,theDeputyDirectorofIPM, who was most helpful in soliciting ?nancial support from the World Mathe- tical Year 2000 National Commission. The Service de Coop eration et d Action Culturelle of the French embassy in Iran kindly provided travel funds for our invited speakers from France. We thank the Service Culturelle for their generous support. Finally,wewouldliketoexpressourgratitudetoM.

Inhalt
Multiple Access Communications Using Combinatorial Designs.- Exact and Approximate Testing/Correcting of Algebraic Functions: A Survey.- The Regularity Lemma and Its Applications in Graph Theory.- Modeling Data and Objects: An Algebraic View Point.- Graph-Theoretical Methods in Computer Vision.- An Introduction to Low-Density Parity-Check Codes.- Primal-Dual Schema Based Approximation Algorithms.- Fourier Transforms and Quantum Computation.