human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "faster sdp hierarchy solvers for local rounding algorithms"):
  Abstract: Convex relaxations based on different hierarchies of linear/semi-definite programs have been used recently to devise approximation algorithms for various optimization problems. The approximation guarantee of these algorithms improves with the number of {\em rounds} $r$ in the hierarchy, though the complexity of solving (or even writing down the solution for) the $r$'th level program grows as $n^{\Omega(r)}$ where $n$ is the input size. #R##N#In this work, we observe that many of these algorithms are based on {\em local} rounding procedures that only use a small part of the SDP solution (of size $n^{O(1)} 2^{O(r)}$ instead of $n^{\Omega(r)}$). We give an algorithm to find the requisite portion in time polynomial in its size. The challenge in achieving this is that the required portion of the solution is not fixed a priori but depends on other parts of the solution, sometimes in a complicated iterative manner. #R##N#Our solver leads to $n^{O(1)} 2^{O(r)}$ time algorithms to obtain the same guarantees in many cases as the earlier $n^{O(r)}$ time algorithms based on $r$ rounds of the Lasserre hierarchy. In particular, guarantees based on $O(\log n)$ rounds can be realized in polynomial time. #R##N#We develop and describe our algorithm in a fairly general abstract framework. The main technical tool in our work, which might be of independent interest in convex optimization, is an efficient ellipsoid algorithm based separation oracle for convex programs that can output a {\em certificate of infeasibility with restricted support}. This is used in a recursive manner to find a sequence of consistent points in nested convex bodies that "fools" local rounding algorithms.

Includes members:
  Member "hypercontractivity sum of squares proofs and their applications":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "sum of squares bounds for the ordering principle")
  Member "rounding semidefinite programming hierarchies via global correlation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "new dependencies of hierarchies in polynomial optimization")
  Member "optimal column based low rank matrix reconstruction":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "improved guarantees and a multiple descent curve for the column subset selection problem and the nystr om method")
  Member "approximating csps with global cardinality constraints using sdp hierarchies":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "new dependencies of hierarchies in polynomial optimization")
  Member "directed steiner tree and the lasserre hierarchy":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "polylogarithmic approximation algorithm for k connected directed steiner tree on quasi bipartite graphs")
  Member "integrality gaps of linear and semi definite programming relaxations for knapsack":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "breaking symmetries to rescue sum of squares the case of makespan scheduling")
  Member "approximating sparsest cut in graphs of bounded treewidth":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "integrality gaps for bounded color matchings")
  Member "efficient volume sampling for row column subset selection":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "improved guarantees and a multiple descent curve for the column subset selection problem and the nystr om method")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.DS(Data Structures and Algorithms)