This book constitutes the proceedings of the 16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013, and the 17th International Workshop on Randomization and Computation, RANDOM 2013, held in August 2013 in the USA. The total of 48 carefully reviewed and selected papers presented in this volume consist of 23 APPROX papers selected out of 46 submissions, and 25 RANDOM papers selected out of 52 submissions. APPROX 2013 focuses on algorithmic and complexity theoretic issues relevant to the development of efficient approximate solutions to computationally difficult problems, while RANDOM 2013 focuses on applications of randomness to computational and combinatorial problems.

This book constitutes the joint refereed proceedings of the 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012, and the 16th International Workshop on Randomization and Computation, RANDOM 2012, held in Cambridge, Massachusetts, USA, in August 2011. The volume contains 28 contributed papers, selected by the APPROX Program Committee out of 70 submissions, and 28 contributed papers, selected by the RANDOM Program Committee out of 67 submissions. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.

This book constitutes the joint refereed proceedings of the 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011, and the 15th International Workshop on Randomization and Computation, RANDOM 2011, held in Princeton, New Jersey, USA, in August 2011. The volume presents 29 revised full papers of the APPROX 2011 workshop, selected from 66 submissions, and 29 revised full papers of the RANDOM 2011 workshop, selected from 64 submissions. They were carefully reviewed and selected for inclusion in the book. In addition two abstracts of invited talks are included. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.

This volume contains the papers presented at the 12th International Wo- shop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2009) and the 13th International Workshop on Randomization and Computation (RANDOM 2009), which took place concurrently at the HP - ditorium in UC Berkeley, USA, during August 21-23, 2009. APPROX focuses on algorithmic and complexity issues surrounding the development of e?cient approximate solutions to computationally di?cult problems, and was the 12th in the series after Aalborg (1998), Berkeley (1999), Saarbru ]cken (2000), Ber- ley (2001), Rome (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), Princeton (2007), and Boston (2008). RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 13th workshop in the series following Bologna (1997), Barcelona (1998), Berkeley(1999), Geneva(2000), Berkeley(2001), Harvard(2002), Prin- ton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), Princeton (2007), and Boston (2008). Topics of interest for APPROX and RANDOM are: design and analysis of approximation algorithms, hardness of approximation, small space algorithms, sub-linear time algorithms, streaming algorithms, embeddings and metric space methods, mathematicalprogrammingmethods, combinatorialproblemsingraphs andnetworks, gametheory, markets, andeconomicapplications, geometricpr- lems, packing, covering, scheduling, approximate learning, design and analysis of online algorithms, randomized complexity theory, pseudorandomness and - randomization, randomcombinatorialstructures, randomwalks/Markovchains, expander graphs and randomness extractors, probabilistic proof systems, err- correctingcodes, average-caseanalysis, propertytesting, computationallearning theory, and other applications of approximation and randomness. The volume contains 25 contributed papers, selected by the APPROX Program Committee out of 56 submissions, and 28 contributed papers, selected by the RANDOM Program Committee out of 57

This volume contains the papers presented at the 11th International Wo- shop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2008) and the 12th International Workshop on Randomization and Computation (RANDOM 2008), which took place concurrently at the MIT (M- sachusetts Institute of Technology) in Boston, USA, during August 25-27, 2008. APPROX focuses on algorithmic and complexity issues surrounding the development of e?cient approximate solutions to computationally di?cult problems, and was the 11th in the series after Aalborg (1998), Berkeley (1999), Saarbru ]cken (2000), Berkeley (2001), Rome (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 12th workshop in the series following Bologna (1997), Barcelona (1998), Berkeley (1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). Topics of interest for APPROX and RANDOM are: design and analysis of - proximation algorithms, hardness of approximation, small space, sub-linear time, streaming, algorithms, embeddings and metric space methods, mathematical programming methods, combinatorial problems in graphs and networks, game t- ory, markets, economic applications, geometric problems, packing, covering, scheduling, approximate learning, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and - beddings, error-correcting codes, average-case analysis, property testing, com- tational learning theory, and other applications of approximation and randomness."

This book constitutes the joint refereed proceedings of the 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and the 11th International Workshop on Randomization and Computation, RANDOM 2007, held in Princeton, NJ, USA, in August 2007.

The 44 revised full papers presented were carefully reviewed and selected from 99 submissions. Topics of interest covered by the papers are design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, geometric problems, game theory and applications, network design and routing, packing and covering, scheduling, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and embeddings, error-correcting codes, average-case analysis, property testing, computational learning theory, and other applications of approximation and randomness.

This book constitutes the joint refereed proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and the 10th International Workshop on Randomization and Computation, RANDOM 2006, held in Barcelona, Spain, in August 2006.

The 44 revised full papers presented were carefully reviewed and selected from 105 submissions. Among the topics covered are design and analysis of approximation algorithms, hardness of approximation problems, small spaces and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, game theory, network design and routing, packing and covering, scheduling, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness, derandomization, random combinatorial structures, Markov chains, prohabalistic proof systems, error-correcting codes, etc.

This book provides a good opportunity for computer science practitioners and researchers to get in sync with the current state-of-the-art and future trends in the field of combinatorial optimization and online algorithms. Recent advances in this area are presented focusing on the design of efficient approximation and on-line algorithms. One central idea in the book is to use a linear program relaxation of the problem, randomization and rounding techniques.

This state-of-the-art survey contains 11 carefully selected papers that cover some classical problems of scheduling, of packing, and of graph theory, but also new optimization problems arising in various applications like networks, data mining or classification.

This volume contains the papers presented at the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2005) and the 9th International Workshop on Randomization and Computation(RANDOM2005), whichtookplaceconcurrentlyattheUniversity of California in Berkeley, on August 22-24, 2005. APPROX focuses on algori- mic and complexity issues surrounding the development of e?cient approximate solutions to computationally hard problems, and APPROX 2005 was the eighth in the series after Aalborg (1998), Berkeley (1999), Saarbru ]cken (2000), Ber- ley (2001), Rome (2002), Princeton(2003), and Cambridge(2004).RANDOM is concerned with applications of randomness to computational and combinatorial problems, and RANDOM 2005 was the ninth workshop in the series foll- ing Bologna (1997), Barcelona (1998), Berkeley(1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), and Cambridge (2004). Topics of interest for APPROX and RANDOM are: design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, geometric problems, game theory and applications, network designandrouting, packingand covering, scheduling, designandanalysisofr- domized algorithms, randomized complexity theory, pseudorandomness and - randomization, random combinatorialstructures, randomwalks/Markovchains, expander graphs and randomness extractors, probabilistic proof systems, r- dom projections and embeddings, error-correcting codes, average-case analysis, property testing, computational learning theory, and other applications of - proximation and randomness. The volume contains 20 contributed papers selected by the APPROX P- gram Committee out of 50 submissions, and 21 contributed papers selected by the RANDOM Program Committee out of 51 submis

Thisvolumecontainsthepaperspresentedatthe7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2004) and the 8th International Workshop on Randomization and Compu- tion (RANDOM 2004), which took place concurrently at Harvard University, Cambridge, on August 22-24, 2004. APPROX focuses on algorithmic and c- plexity issues surrounding the development of e?cient approximate solutions to computationally hard problems, and this year's workshop was the seventh in the series after Aalborg (1998), Berkeley (1999), Saarbru ]cken (2000), Berkeley (2001), Rome (2002), and Princeton (2003). RANDOM is concerned with app- cations of randomness to computational and combinatorial problems, and this year'sworkshopwasthe eighth in the seriesfollowing Bologna(1997), Barcelona (1998), Berkeley (1999), Geneva (2000), Berkeley (2001), Harvard (2002), and Princeton (2003). Topics of interest for APPROX and RANDOM are: design and analysis of approximation algorithms, inapproximability results, approximationclasses, - line problems, small space and data streaming algorithms, sub-linear time al- rithms, embeddings and metric space methods in approximation, math prog- ming in approximation algorithms, coloring and partitioning, cuts and conn- tivity, geometric problems, network design and routing, packing and covering, scheduling, game theory, design and analysis of randomized algorithms, r- domized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projectionsand - beddings, error-correctingcodes, average-caseanalysis, propertytesting, com- tational learning theory, and other applications of approximation and rand- ness. The volumecontains19+18contributed papers, selected by the two program committees from 54+33 submissions received in response to the call for papers."

The Workshop on Approximation and Online Algorithms (WAOA 2003) focused on the design and analysis of algorithms for online and computationally hard problems. Both kinds of problems have a large number of applications ar- ing from a variety of ?elds. The workshop also covered experimental research on approximation and online algorithms. WAOA 2003 took place in Budapest, Hungary, from September 16 to September 18. The workshop was part of the ALGO 2003 event, which also hosted ESA 2003, WABI 2003, and ATMOS 2003. TopicsofinterestforWAOA2003were: competitiveanalysis, inapproximab- ityresults, randomizationtechniques, approximationclasses, scheduling, coloring and partitioning, cuts and connectivity, packing and covering, geometric pr- lems, network design, and applications to game theory and ?nancial problems. In response to our call for papers we received 41 submissions. Each submission was reviewed by at least 3 referees, who judged the papers on originality, quality, and consistency with the topics of the conference. Based on these reviews the program committee selected 19 papers for presentation at the workshop and for publication in this proceedings. This volume contains the 19 selected papers and 5 invited abstracts from an ARACNE minisymposium which took place as part of

This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003.

The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, error-correcting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications.

 This book constitutes the refereed proceedings of the Second International Workshop on Experimental and Efficient Algorithms, WEA 2003, held in Ascona, Switzerland in May 2003. The 19 revised full papers presented together with 3 invited contributions were carefully reviewed and selected from 40 submissions. The focus of the volume is on applications of efficient algorithms for combinatorial problems.

This book constitutes the refereed proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002, held in Rome, Italy in September 2002.The 20 revised full papers presented were carefully reviewed and selected from 54 submissions. Among the topics addressed are design and analysis of approximation algorithms, inapproximability results, online problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and applications to game theory and other fields.

This book constitutes the joint refereed proceedings of the 4th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2001 and of the 5th International Workshop on Ranomization and Approximation Techniques in Computer Science, RANDOM 2001, held in Berkeley, California, USA in August 2001. The 26 revised full papers presented were carefully reviewed and selected from a total of 54 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, on-line problems, randomization, de-randomization, average-case analysis, approximation classes, randomized complexity theory, scheduling, routing, coloring, partitioning, packing, covering, computational geometry, network design, and applications in various fields.

The Workshop on Approximation Algorithms for Combinatorial Optimization ProblemsAPPROX'2000 focuses on algorithmic and complexity aspects ar- ing in the development of e?cient approximate solutions to computationally di?cult problems. It aims, in particular, at fostering cooperation among - gorithmic and complexity researchers in the ?eld. The workshop, to be held at the Max-Planck-Institute for Computer Science in Saarbruc ] ken, Wermany, co-locates with ESA'2020 and WWE'2000. We would like to thank the local organizers at the Max-Planck-Institute (AG 8, Kurt Mehlhorn), for this opp- tunity. APPVOXis an annual meeting, with previousworkshopsin Aalborg and Berkeley. Previous proceedings appeared as LNCS 1464 and 1671. Topics of interest for APPROX'2000 are: design and analysis of appro- mation algorithms, inapproximability results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routingand?owproblems, coloringandiartitioning, cutsandconnectivity, pa- ing and covering, geometric problems, network design, and various applications. The numberof submitted papersto APPROX'2000was68 fromwhich 23 paters were selected. This volume contains the selected papers plus papers by invited speakers. All papers published in the workshop proceedings nere selected by the program committee on the basis of referee reports. Each paper was reviewed vy at least three referees who judged the papers for originality, quality, and consistency with the topics of the conference."

This volume contains the papers presented at the3rd International Wo- shoponRandomizationandApproximationTechniquesinComputer Science (RANDOM 99) and the 2nd International Workshop on - proximation Algorithms for Combinatorial Optimization Problems (APPROX 99), which took place concurrently at the University of California, Berkeley, from August 8 11, 1999. RANDOM 99 is concerned with appli- tions of randomness to computational and combinatorial problems, and is the third workshop in the series following Bologna (1997) and Barcelona (1998). APPROX 99 focuses on algorithmic and complexity issues surrounding the - velopment of e?cient approximate solutions to computationally hard problems, and is the second in the series after Aalborg (1998). The volume contains 24 contributed papers, selected by the two program committees from 44 submissions received in response to the call for papers, together with abstracts of invited lectures by Uri Feige (Weizmann Institute), Christos Papadimitriou (UC Berkeley), Madhu Sudan (MIT), and Avi Wigd- son (Hebrew University and IAS Princeton). We would like to thank all of the authors who submitted papers, our invited speakers, the external referees we consulted and the members of the program committees, who were: RANDOM 99 APPROX 99 Alistair Sinclair, UC Berkeley Dorit Hochbaum, UC Berkeley Noga Alon, Tel Aviv U. Sanjeev Arora, Princeton U. Jennifer Chayes, Microsoft Leslie Hall, Johns Hopkins U. Monika Henzinger, Compaq-SRC Samir Khuller, U. of Maryland Mark Jerrum, U. of Edinburgh Phil Klein, Brown U."

This book constitutes the refereed proceedings of the International Workshop on Approximation Algorithms for Combinatorical Optimization, APPROX'98, held in conjunction with ICALP'98 in Aalborg, Denmark, in July 1998.
The volume presents 14 revised full papers together with three invited papers selected from 37 submissions. The papers address the design and analysis of approximation algorithms, inapproximability results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.

This book constitutes the thoroughly refereed post-workshop proceedings of the 14th International Workshop on Approximation and Online Algorithms, WAOA 2016, held in Aarhus, Denmark, in August 2016 as part of ALGO 2016. The 16 revised full papers presented together with 2 invited lectures were carefully reviewed and selected from 33 submissions. Topics of interest for WAOA 2016 were: coloring and partitioning, competitive analysis, network design, packing and covering, paradigms for design and analysis of approximation and online algorithms, randomization techniques, real world applications, and scheduling problems.

This book constitutes the thoroughly refereed proceedings of the 39th International Workshop on Graph Theoretic Concepts in Computer Science, WG 2013, held in Lubeck, Germany, in June 2013. The 34 revised full papers presented were carefully reviewed and selected from 61 submissions. The book also includes two abstracts. The papers cover a wide range of topics in graph theory related to computer science, such as structural graph theory with algorithmic or complexity applications; design and analysis of sequential, parallel, randomized, parameterized and distributed graph and network algorithms; computational complexity of graph and network problems; computational geometry; graph grammars, graph rewriting systems and graph modeling; graph drawing and layouts; random graphs and models of the web and scale-free networks; and support of these concepts by suitable implementations and applications.

The subject matter of this textbook is the treatment of difficult to solve discrete optimisation problems. The first part presents fast algorithms which can provide approximate solutions to such problems. The second part deals with complexity theory and the non-approximability of optimisation problems. In addition, this textbook contains numerous application examples, exercises, illustrations and sections on the basics such as the Turing machine.