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]

UMLUVENO: V ZS 2017 se koná v pátek od 10:40 v posluchárně S6

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]

5. 1. 2018 (pátek [Friday], 10:40, MFF UK Malá Strana S6)

Wenceslas Fernandez de la Vega and Claire Kenyon-Mathieu: Linear programming relaxations for Maxcut. SODA 2007.
(presented by Jakub Sosnovec)

It is well-known that the integrality gap of the usual linear programming relaxation for Maxcut is 2 - ε. For general graphs, we prove that for any ε and any fixed bound k, adding linear constraints of support bounded by k does not reduce the gap below 2 - ε. We generalize this to prove that for any ε and any fixed bound k, strengthening the usual linear programming relaxation by doing κ rounds of Sherali-Adams lift-and-project does not reduce the gap below 2 - ε. On the other hand, we prove that for dense graphs, this gap drops to 1 + ε after adding all linear constraints of support bounded by some constant depending on ε.

Moses Charikar, Konstantin Makarychev, Yury Makarychev: Integrality Gaps for Sherali-Adams Relaxations. STOC 2009.
(presented by Jakub Sosnovec)

Abstract: We prove strong lower bounds on integrality gaps of Sherali-Adams relaxations for MAX CUT, Vertex Cover, Sparsest Cut and other problems. Our constructions show gaps for Sherali-Adams relaxations that survive nδ rounds of lift and project. For MAX CUT and Vertex Cover, these show that even nδ rounds of Sherali-Adams do not yield a better than 2-ε approximation. The main combinatorial challenge in constructing these gap examples is the construction of a fractional solution that is far from an integer solution, but yet admits consistent distributions of local solutions for all small subsets of variables. Satisfying this consistency requirement is one of the major hurdles to constructing Sherali-Adams gap examples. We present a modular recipe for achieving this, building on previous work on metrics with a local-global structure. We develop a conceptually simple geometric approach to constructing Sherali-Adams gap examples via constructions of consistent local SDP solutions. This geometric approach is surprisingly versatile. We construct Sherali-Adams gap examples for Unique Games based on our construction for MAX CUT together with a parallel repetition like procedure. This in turn allows us to obtain Sherali-Adams gap examples for any problem that has a Unique Games based hardness result (with some additional conditions on the reduction from Unique Games). Using this, we construct 2-ε gap examples for Maximum Acyclic Subgraph that rules out any family of linear constraints with support at most nδ.

Předběžný další program [Preliminary future program]

Martin Skutella: A Note on the Ring Loading Problem. SIAM J. Discrete Math., 30(1), 327-342. 2016.
(presented by Lukáš Folwarczný)

Další články pro ZS 2017 [More papers proposed for this semester]

Euiwoong Lee: Improved Hardness for Cut, Interdiction, and Firefighter Problems. ICALP 2017. Best Student Paper. Also

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

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.

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]

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

Martijn van Ee, Leo van Iersel, Teun Janssen, René Sitters: A priori TSP in the Scenario Model. WAOA 2016: 183-196.

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]