Probabilistic construction of deterministic algorithms: Approximating packing integer programs

1986 ◽  
Author(s):  
Prabhakar Raghavan
Keyword(s):  
Integer Programs ◽  
Deterministic Algorithms ◽  
Packing Integer Programs ◽  
Probabilistic Construction

scholarly journals Algorithms as Mechanisms: The Price of Anarchy of Relax and Round

2020 ◽  
Author(s):  
Paul Dütting ◽  
Thomas Kesselheim ◽  
Éva Tardos
Keyword(s):  
Optimization Problems ◽  
Price Of Anarchy ◽  
Algorithm Design ◽  
Integer Programs ◽  
Flow Problems ◽  
Pricing Rules ◽  
Wide Range ◽  
Packing Integer Programs ◽  
Unsplittable Flow ◽  
The Traveling Salesman Problem

Many algorithms that are originally designed without explicitly considering incentive properties are later combined with simple pricing rules and used as mechanisms. A key question is therefore to understand which algorithms, or, more generally, which algorithm design principles, when combined with simple payment rules such as pay your bid, yield mechanisms with a small price of anarchy. Our main result concerns mechanisms that are based on the relax-and-round paradigm. It shows that oblivious rounding schemes approximately preserve price of anarchy guarantees provable via smoothness. By virtue of our smoothness proofs, our price of anarchy bounds extend to Bayes–Nash equilibria and learning outcomes. In fact, they even apply out of equilibrium, requiring only that agents have no regret for deviations to half their value. We demonstrate the broad applicability of our main result by instantiating it for a wide range of optimization problems ranging from sparse packing integer programs, over single-source unsplittable flow problems and combinatorial auctions with fractionally subadditive valuations, to a maximization variant of the traveling salesman problem.

Approximating disjoint-path problems using packing integer programs

2004 ◽  
Vol 99 (1) ◽  
pp. 63-87 ◽  
Author(s):  
Stavros G. Kolliopoulos ◽  
Clifford Stein
Keyword(s):  
Disjoint Path ◽  
Integer Programs ◽  
Packing Integer Programs

scholarly journals Robust Secretary and Prophet Algorithms for Packing Integer Programs

2022 ◽  
pp. 1273-1297
Author(s):  
C.J. Argue ◽  
Anupam Gupta ◽  
Marco Molinaro ◽  
Sahil Singla
Keyword(s):  
Integer Programs ◽  
Packing Integer Programs

scholarly journals $$\ell _1$$-Sparsity approximation bounds for packing integer programs

2020 ◽  
Vol 183 (1-2) ◽  
pp. 195-214
Author(s):  
Chandra Chekuri ◽  
Kent Quanrud ◽  
Manuel R. Torres
Keyword(s):  
Integer Programs ◽  
Packing Integer Programs

scholarly journals Stochastic packing integer programs with few queries

2019 ◽  
Vol 182 (1-2) ◽  
pp. 141-174 ◽  
Author(s):  
Takanori Maehara ◽  
Yutaro Yamaguchi
Keyword(s):  
Integer Programs ◽  
Packing Integer Programs
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