TheWorkshoponRandomizationandApproximationTechniquesinComputer Science, Random'98, focuses on algorithmic and complexity aspects arising inthedevelopmentofe cientrandomizedsolutionstocomputationallydi cult problems. Itaims,inparticular,atfosteringthecooperationamongpractitioners andtheoreticiansandamongalgorithmicandcomplexityresearchersinthe eld. RANDOM'98,heldattheUniversityofBarcelona(UPC),October8{10,1998, isthesecondintheseries,afterBologna. This volume contains all contributed papers accepted for presentation at theworkshop,togetherwithinvitedlecturesbyJosepD az(UPCBarcelona), AlanM. Frieze(CarnegieMellonU. ),MichaelLuby(ICSIBerkeley),andEmo Welzl(ETHZuric .. h). Thecontributedpaperswereselectedoutofseveraldozen submissions received in response to the call for papers. All papers published intheworkshopproceedingswereselectedbytheprogramcommitteeonthe basisofrefereereports. Considerablee ortwasdevotedtotheevaluationofthe submissionsbytheprogramcommitteeandanumberofotherreferees. Extensive feedbackwasprovidedtoauthorsasaresult,whichwehopehasprovenhelpful tothem. Wewouldliketothankalloftheauthorswhorespondedtothecallforpapers, ourinvitedspeakers,thereferees,andthemembersoftheprogramcommittee: MichaelLuby,Chair,ICSIBerkeley AndreiBroder,DigitalSystemsResearchCenter BernardChazelle,PrincetonU. AndreaClementi,U. ofRome AnnaKarlin,U. ofWashington RichardKarp,U. ofWashington ClaireKenyon,U. ofParisSud MichaelMitzenmacher,DigitalSystemsResearchCenter RajeevMotwani,StanfordU. PrabhakarRaghavan,IBM MariaSerna,UPCBarcelona AlistairSinclair,U. ofCalifornia,Berkeley MadhuSudan,MIT AviWigderson,HebrewU. PeterWinkler,BellLabs WegratefullyacknowledgesupportfromtheEuropeanAssociationINTAS, theComissionatperaUniversitatsiRecerca{GeneralitatdeCatalunya,and Universitat Polit ecnica de Catalunya. Finally, we would like to thank Helena Martinez,CarmeAlvarez,ConradoMartinez,andJordiPetitiSilvestrefortheir helpinthepreparationofthemeeting. August1998 MichaelLuby,Jos eD. P. Rolim,MariaJ. Serna Contents Invited Paper Disjoint Paths in Expander Graphs via Random Walks: A Short Survey 1 AlanM. Frieze RegularPapers A Derandomization Using Min-Wise Independent Permutations 15 AndreiZ. Broder,MosesCharikarandMichaelMitzenmacher An Algorithmic Embedding of Graphs via Perfect Matchings 25 VojtechR.. odl,AndrzejRucin 'skiandMichelleWagner Deterministic Hypergraph Coloring and Its Applications 35 Chi-JenLu On the De-randomization of Space-Bounded Computations 47 RoyArmoni Talagrand's Inequality and Locality in Distributed Computing 60 DevdattP. Dubhashi On-Line Bin-Stretching 71 YossiAzarandOdedRegev Combinatorial Linear Programming: Geometry Can Help 82 BerndGar .. tner A Note on Bounding the Mixing Time by Linear Programming 97 AbrahamSharell Robotic Exploration, Brownian Motion and Electrical Resistance 116 IsraelA. Wagner,MichaelLindenbaumandAlfredM. Bruckstein Fringe Analysis of Synchronized Parallel Algorithms on 2-3 Trees 131 RicardoBaeza-Yates,JoaquimGabarro 'andXavierMesseguer On Balls and Bins with Deletions 145 RichardCole,AlanFrieze,BruceM. Maggs,MichaelMitzenmacher Andr'eaW. Richa,RameshK.

Written by the inventors, Raptor Codes provides a complete introduction to the theory, design and practical implementation of a class of codes that that provide a lot of practical value to a large variety of data communication applications. They find applications in all types of data transmission, including those using the TCP and UDP protocols; multipoint-to-point; point-to-multipoint and multipoint-to-multipoint. The codes are so efficient and practical that two classes of them (R10 and RaptorQ) have been adopted widely by a number of standards bodies and are used in a variety of standards. Different algorithms are introduced for encoding and decoding various versions of these codes, including their systematic versions. Moreover, a hybrid decoding algorithm called ""inactivation decoding"" is introduced which is an integral part of all modern implementations of Raptor codes. There are publicly available specifications that describe exactly how to implement these R10 and RQ codes. However, the standards specifications provide no insight into the rationale for the design choices made. One of the primary purposes of Raptor Codes is to provide this design rationale. Raptor Codes is essential reading for all researchers, engineers and computer scientists designing and implementing data transmission applications. Furthermore, it provides results of extensive simulations of R10 and RQ codes to show the behavior of these codes in many different scenarios.

A pseudorandom generator is an easy-to-compute function that stretches a short random string into a much longer string that "looks" just like a random string to any efficient adversary. One immediate application of a pseudorandom generator is the construction of a private key cryptosystem that is secure against chosen plaintext attack.

There do not seem to be natural examples of functions that are pseudorandom generators. On the other hand, there do seem to be a variety of natural examples of another basic primitive: the one-way function. A function is one-way if it is easy to compute but hard for any efficient adversary to invert on average.

The first half of the book shows how to construct a pseudorandom generator from any one-way function. Building on this, the second half of the book shows how to construct other useful cryptographic primitives, such as private key cryptosystems, pseudorandom function generators, pseudorandom permutation generators, digital signature schemes, bit commitment protocols, and zero-knowledge interactive proof systems. The book stresses rigorous definitions and proofs.