Seminář z aproximačních a online algoritmů
Seminar on Approximation and Online Algorithms

Andreas Emil Feldmann, Petr Kolman, Jiří Sgall

Doba a místo konání [Time and place]

Seminář se koná v úterý od 12:20 v S10. [Seminar takes place on Tuesday 12:20 in S10]

Oznámení o seminářích se distribuuje pomocí mailing listu, do kterého se můžete zapsat na adrese
You can subscribe to the mailing list with the seminar anouncement at

Kontakt, tel. 951 554 372;, tel. 951 554 155;, tel. 951 554 293.

Nejbližší program semináře [Next program]

No seminar on Dec 4 and Dec 11

Dec 18, 2018 (úterý [Tuesday], 12:20, MFF UK Malá Strana S10)

Michael Lampis: Parameterized Approximation Schemes using Graph Widths.
(presented by Michal Berg)

Abstract: Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability of a number of problems which are known to be hard to solve exactly when parameterized by treewidth or clique-width. Our main contribution is to present a natural randomized rounding technique that extends well-known ideas and can be used for both of these widths. Applying this very generic technique we obtain approximation schemes for a number of problems, evading both polynomial-time inapproximability and parameterized intractability bounds.

Předběžný další program [Preliminary future program]

Andreas Wiese: A (1+eps)-approximation for Unsplittable Flow on a Path in fixed-parameter running time. ICALP 2017.
(presented by Lukáš Folwarczný)

Abstract: Unsplittable Flow on a Path (UFP) is a well-studied problem. It arises in many different settings such as bandwidth allocation, scheduling, and caching. We are given a path with capacities on the edges and a set of tasks, each of them is described by a start and an end vertex and a demand. The goal is to select as many tasks as possible such that the demand of the selected tasks using each edge does not exceed the capacity of this edge. The problem admits a QPTAS and the best known polynomial time result is a (2+epsilon)-approximation. As we prove in this paper, the problem is intractable for fixed-parameter algorithms since it is W[1]-hard. A PTAS seems difficult to construct. However, we show that if we combine the paradigms of approximation algorithms and fixed-parameter tractability we can break the mentioned boundaries. We show that on instances with |OPT|=k we can compute a (1+epsilon)-approximation in time 2^O(k log k)n^O_epsilon(1) log(u_max) (where u_max is the maximum edge capacity). To obtain this algorithm we develop new insights for UFP and enrich a recent dynamic programming framework for the problem. Our results yield a PTAS for (unweighted) UFP instances where |OPT| is at most O(log n/log log n) and they imply that the problem does not admit an EPTAS, unless W[1]=FPT.

Hans-Joachim Bockenhauer, Juraj Hromkovic, Joachim Kneis, Joachim Kupke: The Parameterized Approximability of TSP with Deadlines. Theory of Computing Systems 41:431–444, 2007.
(presented by Petr Vincena)

Další články pro ZS 2018 [More papers proposed for this semester]

Key papers (which may not be too easy to read):

Sanjeev Arora: Polynomial Time Approximation Schemes for Euclidean
Traveling Salesman and Other Geometric Problems
JACM 45:753–782, 1998.

Parinya Chalermsook, Marek Cygan, Guy Kortsarz, Bundit Laekhanukit, Pasin Manurangsi, Danupon Nanongkai, Luca Trevisan: From Gap-ETH to FPT-Inapproximability: Clique, Dominating Set, and More.

Some (hopefully) easier papers:

Anupam Gupta, Euiwoong Lee, Jason Li: An FPT Algorithm Beating 2-Approximation for k-Cut.

Samozřejmě, jako vždy, jsou vítany jsou i další náměty, zejména pak prezentace vlastních výsledků účastníků semináře.

Další články, o kterých jsme uvažovali, zbylé z minulého semestru atd.
[Additional proposed papers, leftovers from the last semester]

Parinya Chalermsook, Marek Cygan, Guy Kortsarz, Bundit Laekhanukit, Pasin Manurangsi, Danupon Nanongkai, Luca Trevisan: From Gap-ETH to FPT-Inapproximability: Clique, Dominating Set, and More. FOCS 2017. Also

Michael Lampis: Parameterized Approximation Schemes using Graph Widths. ICALP 2014. Also

Alice Paul, Daniel Freund, Aaron Ferber, David Shmoys and David Williamson: Prize-Collecting TSP with a Budget Constraint. ESA 2017.

Klaus Jansen and Lars Rohwedder: On the Configuration-LP of the Restricted Assignment Problem. SODA 2017: 2670-2678, also

Alantha Newman, Heiko Röglin, and Johanna Seif: The Alternating Stock Size Problem and the Gasoline Puzzle. ESA 2016. Also

János Balogh, József Békési, György Dósa, Leah Epstein, Asaf Levin: Online bin packing with cardinality constraints resolved. At

Harald Räcke: Optimal hierarchical decompositions for congestion minimization in networks. STOC 2008:255-264. Also here.

Jittat Fakcheroenphol, Kunal Talwar and Satish Rao: A tight bound on approximating arbitrary metrics by tree metrics. STOC 2003, J. Comput. Syst. Sci. 69(3): 485-497 (2004).

Předchozí program semináře [Past program]