TY - GEN

T1 - Improved approximation guarantees through higher levels of SDP hierarchies

AU - Chlamtac, Eden

AU - Singh, Gyanit

PY - 2008/9/22

Y1 - 2008/9/22

N2 - For every fixed γ ≥ 0, we give an algorithm that, given an n-vertex 3-uniform hypergraph containing an independent set of size γn, finds an independent set of size . This improves upon a recent result of Chlamtac, which, for a fixed ε > 0, finds an independent set of size n ε in any 3-uniform hypergraph containing an independent set of size . The main feature of this algorithm is that, for fixed γ, it uses the Θ(1/γ 2)-level of a hierarchy of semidefinite programming (SDP) relaxations. On the other hand, we show that for at least one hierarchy which gives such a guarantee, 1/γ levels yield no non-trivial guarantee. Thus, this is a first SDP-based algorithm for which the approximation guarantee improves indefinitely as one uses progressively higher-level relaxations.

AB - For every fixed γ ≥ 0, we give an algorithm that, given an n-vertex 3-uniform hypergraph containing an independent set of size γn, finds an independent set of size . This improves upon a recent result of Chlamtac, which, for a fixed ε > 0, finds an independent set of size n ε in any 3-uniform hypergraph containing an independent set of size . The main feature of this algorithm is that, for fixed γ, it uses the Θ(1/γ 2)-level of a hierarchy of semidefinite programming (SDP) relaxations. On the other hand, we show that for at least one hierarchy which gives such a guarantee, 1/γ levels yield no non-trivial guarantee. Thus, this is a first SDP-based algorithm for which the approximation guarantee improves indefinitely as one uses progressively higher-level relaxations.

UR - http://www.scopus.com/inward/record.url?scp=51849124187&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85363-3_5

DO - 10.1007/978-3-540-85363-3_5

M3 - Conference contribution

AN - SCOPUS:51849124187

SN - 3540853626

SN - 9783540853626

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 49

EP - 62

BT - Approximation, Randomization and Combinatorial Optimization

T2 - 11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008

Y2 - 25 August 2008 through 27 August 2008

ER -