This book constitutes the revised selected papers of the 20th International Workshop on Combinatorial Algorithms, held in June/July 2009 in the castle of Hradec nad Moravici, Czech Republic.

The 41 papers included in this volume together with 5 invited papers were carefully reviewed and selected from over 100 submissions. The topics dealt with are algorithms and data structures, applications, combinatorial enumeration, combinatorial optimization, complexity theory, computational biology, databases, decompositions and combinatorial designs, discrete and computational geometry, including graph drawing, and graph theory and combinatorics.

The 7th Annual Conference on Theory and Applications of Models of Compu- tion was held during June 7-11, 2010 in Prague. After six successful conferences held in 2004-2009 in China (Beijing, Kunming, Beijing, Shanghai, Xi'an, and ChangSha) TAMC left Asia for the ?rst time, aiming at the "heart of Europe. " Changingthegeographicallocationdidnotbringanychangestothescopeofthe conference. Its three main themes continued to be Computability, Complexity, and Algorithms. The conference aims to bring together researchersfrom all over the world with interests in theoretical computer science, algorithmic mathem- ics,andapplicationsto thephysicalsciences. Thisyearwesawmoreparticipants from Europe and the Americas, but we were very happy that we could also w- come to Prague traditional participants from Asia (China, Japan, and India) to continue enhancing the collaboration among the theoretical computer science communities of these continents. After hard work the Program Committee decided to accept 35 papers out of 76 submitted to TAMC 2010. Each submission was reviewed by at least three, Program Committee members. All actions of the Program Committee were - ordinated via ?awlessly and e?ciently running EasyChair. We congratulate the authors of accepted contributions and thank all authors who submitted their papers. They all contributed to a successful event. We extend our thanks to the distinguished plenary speakers who accepted our invitation to deliver plenary talks - John Hopcroft from Cornell University and Shang-Hua Teng from University of Southern California. Their talks "New Research Directions in the Information Age" and "The Laplacian Paradigm: Emerging Algorithms for Massive Graph" were highlights of the conference.

This volume contains the papers presented at the 29th Symposium on Mat- matical Foundations of Computer Science, MFCS 2004, held in Prague, Czech Republic, August 22-27, 2004. The conference was organized by the Institute for Theoretical Computer Science (ITI) and the Department of Theoretical Com- terScienceandMathematicalLogic(KTIML)oftheFacultyofMathematicsand Physics of Charles University in Prague. It was supported in part by the Eu- pean Association for Theoretical Computer Science (EATCS) and the European Research Consortium for Informatics and Mathematics (ERCIM). Traditionally, the MFCS symposia encourage high-quality research in all branches of theoretical computer science. Ranging in scope from automata, f- mal languages, data structures, algorithms and computational geometry to c- plexitytheory, modelsofcomputation, andapplicationsincludingcomputational biology, cryptography, security and arti?cial intelligence, the conference o?ers a unique opportunity to researchers from diverse areas to meet and present their results to a general audience. The scienti?c program of this year's MFCS took place in the lecture halls of the recently reconstructed building of the Faculty of Mathematics and P- sics in the historical center of Prague, with the famous Prague Castle and other celebratedhistoricalmonumentsinsight.Theviewfromthewindowswasach- lengingcompetitionforthespeakersinthe?ghtfortheattentionoftheaudience. But we did not fear the result: Due to the unusually tough competition for this year's MFCS, the admitted presentations certainly attracted considerable in- rest. The conference program (and the proceedings) consisted of 60 contributed papers selected by the Program Committee from a total of 167 submissions.