Theoretical Aspects of Computer Science Advanced Lectures

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) 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.