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Paul W. Goldberg
Paul Goldberg 0001
Person information
- affiliation: University of Oxford, Department of Computer Science, UK
- affiliation (former): University of Liverpool, Department of Computer Science, UK
Other persons with the same name
- Paul Goldberg 0002
— IEEE Robotics and Automation Society, New York City, NY, USA
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2020 – today
- 2024
- [j51]Elizabeth Baldwin
, Paul W. Goldberg
, Paul Klemperer
, Edwin Lock
:
Solving Strong-Substitutes Product-Mix Auctions. Math. Oper. Res. 49(3): 1502-1534 (2024) - [c76]Emanuel Tewolde, Brian Hu Zhang, Caspar Oesterheld, Manolis Zampetakis, Tuomas Sandholm, Paul Goldberg, Vincent Conitzer:
Imperfect-Recall Games: Equilibrium Concepts and Their Complexity. IJCAI 2024: 2994-3004 - [c75]John Fearnley
, Paul W. Goldberg
, Alexandros Hollender
, Rahul Savani
:
The Complexity of Computing KKT Solutions of Quadratic Programs. STOC 2024: 892-903 - [i62]Edith Elkind, Abheek Ghosh, Paul W. Goldberg:
Continuous-Time Best-Response and Related Dynamics in Tullock Contests with Convex Costs. CoRR abs/2402.08541 (2024) - [i61]Emanuel Tewolde, Brian Hu Zhang, Caspar Oesterheld, Manolis Zampetakis, Tuomas Sandholm, Paul W. Goldberg, Vincent Conitzer:
Imperfect-Recall Games: Equilibrium Concepts and Their Complexity. CoRR abs/2406.15970 (2024) - [i60]Edwin Lock, Benjamin Patrick Evans, Eleonora Kreacic, Sujay Bhatt, Alec Koppel, Sumitra Ganesh, Paul W. Goldberg:
Decentralized Convergence to Equilibrium Prices in Trading Networks. CoRR abs/2412.13972 (2024) - 2023
- [j50]John Fearnley
, Paul Goldberg
, Alexandros Hollender
, Rahul Savani
:
The Complexity of Gradient Descent: CLS = PPAD ∩ PLS. J. ACM 70(1): 7:1-7:74 (2023) - [j49]Paul W. Goldberg
, Matthew J. Katzman
:
Lower bounds for the query complexity of equilibria in Lipschitz games. Theor. Comput. Sci. 962: 113931 (2023) - [j48]Paul W. Goldberg
, Matthew J. Katzman
:
PPAD-complete approximate pure Nash equilibria in Lipschitz games. Theor. Comput. Sci. 980: 114218 (2023) - [c74]Emanuel Tewolde, Caspar Oesterheld, Vincent Conitzer, Paul W. Goldberg:
The Computational Complexity of Single-Player Imperfect-Recall Games. IJCAI 2023: 2878-2887 - [c73]Paul Goldberg
, Jiawei Li:
Consensus Division in an Arbitrary Ratio. ITCS 2023: 57:1-57:18 - [c72]Paul W. Goldberg
, Kasper Høgh
, Alexandros Hollender
:
The Frontier of Intractability for EFX with Two Agents. SAGT 2023: 290-307 - [c71]Abheek Ghosh
, Paul W. Goldberg
:
Best-Response Dynamics in Lottery Contests. EC 2023: 736 - [i59]Paul W. Goldberg, Kasper Høgh, Alexandros Hollender:
The Frontier of Intractability for EFX with Two Agents. CoRR abs/2301.10354 (2023) - [i58]Abheek Ghosh, Paul W. Goldberg:
Best-Response Dynamics in Lottery Contests. CoRR abs/2305.10881 (2023) - [i57]Emanuel Tewolde, Caspar Oesterheld, Vincent Conitzer, Paul W. Goldberg:
The Computational Complexity of Single-Player Imperfect-Recall Games. CoRR abs/2305.17805 (2023) - [i56]Simon Finster, Paul W. Goldberg
, Edwin Lock:
Substitutes markets with budget constraints: solving for competitive and optimal prices. CoRR abs/2310.03692 (2023) - [i55]John Fearnley, Paul W. Goldberg
, Alexandros Hollender, Rahul Savani
:
The Complexity of Computing KKT Solutions of Quadratic Programs. CoRR abs/2311.13738 (2023) - 2022
- [j47]Paul W. Goldberg
, Alexandros Hollender
, Ayumi Igarashi, Pasin Manurangsi, Warut Suksompong
:
Consensus Halving for Sets of Items. Math. Oper. Res. 47(4): 3357-3379 (2022) - [j46]Edwin Lock
, Paul W. Goldberg
, Francisco J. Marmolejo Cossío
:
Learning Strong Substitutes Demand via Queries. ACM Trans. Economics and Comput. 10(2): 10:1-10:22 (2022) - [c70]Edith Elkind, Abheek Ghosh, Paul Goldberg:
Complexity of Deliberative Coalition Formation. AAAI 2022: 4975-4982 - [c69]Edith Elkind, Abheek Ghosh, Paul W. Goldberg:
Contests to Incentivize a Target Group. IJCAI 2022: 279-285 - [c68]Edith Elkind, Abheek Ghosh, Paul W. Goldberg
:
Simultaneous Contests with Equal Sharing Allocation of Prizes: Computational Complexity and Price of Anarchy. SAGT 2022: 133-150 - [c67]Paul W. Goldberg
, Matthew J. Katzman
:
PPAD-Complete Pure Approximate Nash Equilibria in Lipschitz Games. SAGT 2022: 169-186 - [i54]Paul W. Goldberg, Jiawei Li:
Consensus Division in an Arbitrary Ratio. CoRR abs/2202.06949 (2022) - [i53]Edith Elkind, Abheek Ghosh, Paul Goldberg:
Complexity of Deliberative Coalition Formation. CoRR abs/2202.12594 (2022) - [i52]Edith Elkind, Abheek Ghosh, Paul Goldberg
:
Contests to Incentivize a Target Group. CoRR abs/2204.14051 (2022) - [i51]Edith Elkind, Abheek Ghosh, Paul W. Goldberg
:
Simultaneous Contests with Equal Sharing Allocation of Prizes: Computational Complexity and Price of Anarchy. CoRR abs/2207.08151 (2022) - [i50]Paul W. Goldberg
, Matthew J. Katzman:
PPAD-Complete Pure Approximate Nash Equilibria in Lipschitz Games. CoRR abs/2207.09962 (2022) - 2021
- [j45]Paul W. Goldberg
, Alexandros Hollender
:
The Hairy Ball problem is PPAD-complete. J. Comput. Syst. Sci. 122: 34-62 (2021) - [j44]Paul W. Goldberg
, Francisco J. Marmolejo Cossío:
Learning Convex Partitions and Computing Game-theoretic Equilibria from Best-response Queries. ACM Trans. Economics and Comput. 9(1): 3:1-3:36 (2021) - [c66]Paul W. Goldberg
, Matthew J. Katzman
:
Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games. SAGT 2021: 124-139 - [c65]John Fearnley, Paul W. Goldberg
, Alexandros Hollender
, Rahul Savani
:
The complexity of gradient descent: CLS = PPAD ∩ PLS. STOC 2021: 46-59 - [c64]Edith Elkind, Abheek Ghosh, Paul W. Goldberg:
Contest Design with Threshold Objectives. WINE 2021: 554 - [i49]Paul W. Goldberg, Matthew J. Katzman:
Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games. CoRR abs/2107.03898 (2021) - [i48]Paul W. Goldberg, Ioana Iaru:
Equivalence of Models of Cake-Cutting Protocols. CoRR abs/2108.03641 (2021) - [i47]Edith Elkind, Abheek Ghosh, Paul W. Goldberg:
Contest Design with Threshold Objectives. CoRR abs/2109.03179 (2021) - 2020
- [j43]Paul W. Goldberg
, Alexandros Hollender
, Warut Suksompong:
Contiguous Cake Cutting: Hardness Results and Approximation Algorithms. J. Artif. Intell. Res. 69: 109-141 (2020) - [j42]Luka Gligic, Andrey Kormilitzin, Paul Goldberg
, Alejo J. Nevado-Holgado
:
Named entity recognition in electronic health records using transfer learning bootstrapped Neural Networks. Neural Networks 121: 132-139 (2020) - [j41]Riccardo Colini-Baldeschi, Paul W. Goldberg
, Bart de Keijzer, Stefano Leonardi, Tim Roughgarden, Stefano Turchetta:
Approximately Efficient Two-Sided Combinatorial Auctions. ACM Trans. Economics and Comput. 8(1): 4:1-4:29 (2020) - [c63]Paul W. Goldberg, Alexandros Hollender
, Warut Suksompong:
Contiguous Cake Cutting: Hardness Results and Approximation Algorithms. AAAI 2020: 1990-1997 - [c62]Paul W. Goldberg
, Alexandros Hollender
, Ayumi Igarashi, Pasin Manurangsi, Warut Suksompong:
Consensus Halving for Sets of Items. WINE 2020: 384-397 - [c61]Paul W. Goldberg
, Edwin Lock
, Francisco J. Marmolejo Cossío
:
Learning Strong Substitutes Demand via Queries. WINE 2020: 401-415 - [i46]Paul W. Goldberg, Edwin Lock
, Francisco J. Marmolejo Cossío:
Learning Strong Substitutes Demand via Queries. CoRR abs/2005.01496 (2020) - [i45]Paul W. Goldberg, Alexandros Hollender, Ayumi Igarashi, Pasin Manurangsi, Warut Suksompong:
Consensus Halving for Sets of Items. CoRR abs/2007.06754 (2020) - [i44]John Fearnley, Paul W. Goldberg, Alexandros Hollender, Rahul Savani
:
The Complexity of Gradient Descent: CLS = PPAD ∩ PLS. CoRR abs/2011.01929 (2020)
2010 – 2019
- 2019
- [j40]Paul W. Goldberg
, Francisco J. Marmolejo Cossío, Zhiwei Steven Wu
:
Logarithmic Query Complexity for Approximate Nash Computation in Large Games. Theory Comput. Syst. 63(1): 26-53 (2019) - [j39]Aris Filos-Ratsikas, Paul W. Goldberg:
The Complexity of Necklace Splitting, Consensus-Halving, and Discrete Ham Sandwich. SIAM J. Comput. 52(on): STOC19-200-STOC19-268 (2019) - [c60]Matthias Gerstgrasser, Paul W. Goldberg
, Bart de Keijzer, Philip Lazos, Alexander Skopalik:
Multi-Unit Bilateral Trade. AAAI 2019: 1973-1980 - [c59]Paul W. Goldberg
, Alexandros Hollender
:
The Hairy Ball Problem is PPAD-Complete. ICALP 2019: 65:1-65:14 - [c58]Aris Filos-Ratsikas
, Paul W. Goldberg
:
The complexity of splitting necklaces and bisecting ham sandwiches. STOC 2019: 638-649 - [i43]Luka Gligic, Andrey Kormilitzin, Paul Goldberg, Alejo J. Nevado-Holgado:
Named Entity Recognition in Electronic Health Records Using Transfer Learning Bootstrapped Neural Networks. CoRR abs/1901.01592 (2019) - [i42]Paul W. Goldberg, Alexandros Hollender:
The Hairy Ball Problem is PPAD-Complete. CoRR abs/1902.07657 (2019) - [i41]Elizabeth Baldwin, Paul W. Goldberg, Paul Klemperer, Edwin Lock
:
Solving Strong-Substitutes Product-Mix Auctions. CoRR abs/1909.07313 (2019) - [i40]Paul W. Goldberg, Alexandros Hollender, Warut Suksompong:
Contiguous Cake Cutting: Hardness Results and Approximation Algorithms. CoRR abs/1911.05416 (2019) - 2018
- [j38]Paul W. Goldberg
, Christos H. Papadimitriou:
Towards a unified complexity theory of total functions. J. Comput. Syst. Sci. 94: 167-192 (2018) - [c57]Paul W. Goldberg
, Christos H. Papadimitriou:
Towards a Unified Complexity Theory of Total Functions. ITCS 2018: 37:1-37:20 - [c56]Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg
, Jie Zhang
:
Hardness Results for Consensus-Halving. MFCS 2018: 24:1-24:16 - [c55]Aris Filos-Ratsikas
, Paul W. Goldberg
:
Consensus halving is PPA-complete. STOC 2018: 51-64 - [c54]Paul W. Goldberg
, Francisco J. Marmolejo Cossío
:
Learning Convex Partitions and Computing Game-Theoretic Equilibria from Best Response Queries. WINE 2018: 168-187 - [i39]Aris Filos-Ratsikas, Paul W. Goldberg:
The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches. CoRR abs/1805.12559 (2018) - [i38]Paul W. Goldberg, Francisco J. Marmolejo Cossío:
Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries. CoRR abs/1807.06170 (2018) - [i37]Matthias Gerstgrasser, Paul W. Goldberg, Bart de Keijzer, Philip Lazos, Alexander Skopalik:
Multi-unit Bilateral Trade. CoRR abs/1811.05130 (2018) - [i36]Maximilian Hofer, Andrey Kormilitzin, Paul W. Goldberg, Alejo J. Nevado-Holgado:
Few-shot Learning for Named Entity Recognition in Medical Text. CoRR abs/1811.05468 (2018) - [i35]Alexandros Hollender, Paul W. Goldberg:
The Complexity of Multi-source Variants of the End-of-Line Problem, and the Concise Mutilated Chessboard. Electron. Colloquium Comput. Complex. TR18 (2018) - 2017
- [j37]Xiaotie Deng
, Paul W. Goldberg
, Yang Sun, Bo Tang, Jinshan Zhang:
Pricing ad slots with consecutive multi-unit demand. Auton. Agents Multi Agent Syst. 31(3): 584-605 (2017) - [j36]Paul W. Goldberg
, Stefano Turchetta
:
Query complexity of approximate equilibria in anonymous games. J. Comput. Syst. Sci. 90: 80-98 (2017) - [c53]Haris Aziz
, Paul Goldberg
, Toby Walsh:
Equilibria in Sequential Allocation. ADT 2017: 270-283 - [c52]Paul W. Goldberg
, Christos H. Papadimitriou:
TFNP: An Update. CIAC 2017: 3-9 - [c51]Riccardo Colini-Baldeschi, Paul W. Goldberg
, Bart de Keijzer, Stefano Leonardi, Tim Roughgarden, Stefano Turchetta:
Approximately Efficient Two-Sided Combinatorial Auctions. EC 2017: 591-608 - [c50]Riccardo Colini-Baldeschi, Paul W. Goldberg
, Bart de Keijzer, Stefano Leonardi, Stefano Turchetta:
Fixed Price Approximability of the Optimal Gain from Trade. WINE 2017: 146-160 - [i34]Haris Aziz, Paul Goldberg, Toby Walsh:
Equilibria in Sequential Allocation. CoRR abs/1705.09444 (2017) - [i33]Riccardo Colini-Baldeschi, Paul W. Goldberg, Bart de Keijzer, Stefano Leonardi, Stefano Turchetta:
Fixed Price Approximability of the Optimal Gain From Trade. CoRR abs/1710.08394 (2017) - [i32]Aris Filos-Ratsikas, Paul W. Goldberg:
Consensus Halving is PPA-Complete. CoRR abs/1711.04503 (2017) - [i31]Paul W. Goldberg, Yishay Mansour, Paul Dütting:
Game Theory Meets Computational Learning Theory (Dagstuhl Seminar 17251). Dagstuhl Reports 7(6): 68-85 (2017) - [i30]Paul W. Goldberg, Christos H. Papadimitriou:
Towards a Unified Complexity Theory of Total Functions. Electron. Colloquium Comput. Complex. TR17 (2017) - 2016
- [j35]John Fearnley, Paul W. Goldberg
, Rahul Savani
, Troels Bjerre Sørensen:
Approximate Well-supported Nash Equilibria Below Two-thirds. Algorithmica 76(2): 297-319 (2016) - [j34]Xiaotie Deng
, Paul W. Goldberg
, Bo Tang, Jinshan Zhang:
Multi-Unit Bayesian Auction with Demand or Budget Constraints. Comput. Intell. 32(3): 355-368 (2016) - [j33]Paul Goldberg:
EATCS Fellows 2017 - Call for Nominations. Bull. EATCS 120 (2016) - [j32]Ning Chen, Xiaotie Deng
, Paul W. Goldberg
, Jinshan Zhang:
On revenue maximization with sharp multi-unit demands. J. Comb. Optim. 31(3): 1174-1205 (2016) - [j31]Diodato Ferraioli, Paul W. Goldberg
, Carmine Ventre
:
Decentralized dynamics for finite opinion games. Theor. Comput. Sci. 648: 96-115 (2016) - [j30]Paul W. Goldberg
, Aaron Roth
:
Bounds for the Query Complexity of Approximate Equilibria. ACM Trans. Economics and Comput. 4(4): 24:1-24:25 (2016) - [c49]George Christodoulou
, Aris Filos-Ratsikas
, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg
, Jie Zhang
, Jinshan Zhang:
Social Welfare in One-Sided Matching Mechanisms. AAMAS Workshops (Selected Papers) 2016: 30-50 - [c48]George Christodoulou, Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, Jie Zhang, Jinshan Zhang:
Social Welfare in One-Sided Matching Mechanisms: (Extended Abstract). AAMAS 2016: 1297-1298 - [c47]Baharak Rastegari, Paul Goldberg, David F. Manlove:
Preference Elicitation in Matching Markets via Interviews: A Study of Offline Benchmarks (Extended Abstract). AAMAS 2016: 1393-1394 - [c46]Paul W. Goldberg
, Francisco J. Marmolejo Cossío
, Zhiwei Steven Wu:
Logarithmic Query Complexity for Approximate Nash Computation in Large Games. SAGT 2016: 3-14 - [c45]Matthias Gerstgrasser, Paul W. Goldberg
, Elias Koutsoupias:
Revenue Maximization for Market Intermediation with Correlated Priors. SAGT 2016: 273-285 - [i29]Baharak Rastegari, Paul Goldberg, David F. Manlove:
Preference Elicitation in Matching Markets via Interviews: A Study of Offline Benchmarks. CoRR abs/1602.04792 (2016) - [i28]Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, Jie Zhang:
Hardness Results for Consensus-Halving. CoRR abs/1609.05136 (2016) - [i27]Paul W. Goldberg, Francisco J. Marmolejo Cossío, Zhiwei Steven Wu:
Logarithmic Query Complexity for Approximate Nash Computation in Large Games. CoRR abs/1610.08906 (2016) - [i26]Riccardo Colini-Baldeschi, Paul W. Goldberg, Bart de Keijzer, Stefano Leonardi, Tim Roughgarden, Stefano Turchetta:
Approximately Efficient Two-Sided Combinatorial Auctions. CoRR abs/1611.05342 (2016) - 2015
- [j29]John Fearnley, Martin Gairing, Paul W. Goldberg, Rahul Savani:
Learning equilibria of games via payoff queries. J. Mach. Learn. Res. 16: 1305-1344 (2015) - [c44]Paul W. Goldberg
, Bo Tang:
Auction Design with a Revenue Target. SAGT 2015: 137-149 - [c43]Paul W. Goldberg
:
Algorithmic Game Theory (Tutorial). STACS 2015: 20-20 - [c42]Paul W. Goldberg
, Stefano Turchetta:
Query Complexity of Approximate Equilibria in Anonymous Games. WINE 2015: 357-369 - [i25]George Christodoulou, Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, Jie Zhang, Jinshan Zhang:
Welfare Ratios in One-Sided Matching Mechanisms. CoRR abs/1502.03849 (2015) - [i24]Paul W. Goldberg:
The Complexity of the Path-following Solutions of Two-dimensional Sperner/Brouwer Functions. CoRR abs/1506.04882 (2015) - 2014
- [j28]Paul W. Goldberg
, Arnoud Pastink
:
On the communication complexity of approximate Nash equilibria. Games Econ. Behav. 85: 19-31 (2014) - [j27]Xiaotie Deng
, Paul W. Goldberg
, Bo Tang, Jinshan Zhang:
Revenue maximization in a Bayesian double auction market. Theor. Comput. Sci. 539: 1-12 (2014) - [c41]Paul W. Goldberg
, Aaron Roth
:
Bounds for the query complexity of approximate equilibria. EC 2014: 639-656 - [i23]Paul W. Goldberg, Stefano Turchetta:
Query Complexity of Approximate Equilibria in Anonymous Games. CoRR abs/1412.6455 (2014) - 2013
- [j26]Paul W. Goldberg
, Rahul Savani
, Troels Bjerre Sørensen, Carmine Ventre
:
On the approximation performance of fictitious play in finite games. Int. J. Game Theory 42(4): 1059-1083 (2013) - [j25]Leslie Ann Goldberg, Paul W. Goldberg
, Piotr Krysta, Carmine Ventre
:
Ranking games that have competitiveness-based strategies. Theor. Comput. Sci. 476: 24-37 (2013) - [j24]Paul W. Goldberg, Christos H. Papadimitriou, Rahul Savani
:
The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions. ACM Trans. Economics and Comput. 1(2): 9:1-9:25 (2013) - [c40]Paul W. Goldberg, Carmine Ventre:
Using lotteries to approximate the optimal revenue. AAMAS 2013: 643-650 - [c39]Paul W. Goldberg
, Antony McCabe:
Shortest Paths with Bundles and Non-additive Weights Is Hard. CIAC 2013: 264-275 - [c38]Xiaotie Deng
, Paul W. Goldberg
, Yang Sun, Bo Tang, Jinshan Zhang:
Pricing Ad Slots with Consecutive Multi-unit Demand. SAGT 2013: 255-266 - [c37]John Fearnley, Martin Gairing, Paul Goldberg
, Rahul Savani
:
Learning equilibria of games via payoff queries. EC 2013: 397-414 - [i22]Leslie Ann Goldberg, Paul W. Goldberg, Piotr Krysta, Carmine Ventre:
Ranking Games that have Competitiveness-based Strategies. CoRR abs/1301.5844 (2013) - [i21]John Fearnley, Martin Gairing, Paul W. Goldberg, Rahul Savani
:
Learning Equilibria of Games via Payoff Queries. CoRR abs/1302.3116 (2013) - [i20]Paul W. Goldberg, Arnoud Pastink:
On the Communication Complexity of Approximate Nash Equilibria. CoRR abs/1302.3793 (2013) - [i19]Xiaotie Deng, Paul W. Goldberg, Yang Sun, Bo Tang, Jinshan Zhang:
Pricing Ad Slots with Consecutive Multi-unit Demand. CoRR abs/1308.1382 (2013) - [i18]Diodato Ferraioli, Paul W. Goldberg, Carmine Ventre:
Decentralized Dynamics for Finite Opinion Games. CoRR abs/1311.1610 (2013) - [i17]Paul W. Goldberg, Aaron Roth:
Bounds for the Query Complexity of Approximate Equilibria. Electron. Colloquium Comput. Complex. TR13 (2013) - 2012
- [c36]Xiaotie Deng, Paul W. Goldberg
, Bo Tang, Jinshan Zhang:
Revenue Maximization in a Bayesian Double Auction Market. ISAAC 2012: 690-699 - [c35]John Fearnley, Paul W. Goldberg
, Rahul Savani
, Troels Bjerre Sørensen:
Approximate Well-Supported Nash Equilibria Below Two-Thirds. SAGT 2012: 108-119 - [c34]Diodato Ferraioli
, Paul W. Goldberg
, Carmine Ventre
:
Decentralized Dynamics for Finite Opinion Games. SAGT 2012: 144-155 - [c33]Paul W. Goldberg
, Antony McCabe:
Commodity Auctions and Frugality Ratios. SAGT 2012: 180-191 - [c32]Paul W. Goldberg
, Arnoud Pastink:
On the Communication Complexity of Approximate Nash Equilibria. SAGT 2012: 192-203 - [e1]Paul W. Goldberg:
Internet and Network Economics - 8th International Workshop, WINE 2012, Liverpool, UK, December 10-12, 2012. Proceedings. Lecture Notes in Computer Science 7695, Springer 2012, ISBN 978-3-642-35310-9 [contents] - [i16]