TY - GEN
T1 - Lower bounds for approximating graph parameters via communication complexity
AU - Eden, Talya
AU - Rosenbaum, Will
N1 - Publisher Copyright:
© 2018 Aditya Bhaskara and Srivatsan Kumar.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - In a celebrated work, Blais, Brody, and Matulef [7] developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower bounds as well as simplified analyses of known lower bounds. Here, we take a further step in generalizing the methodology of [7] to analyze the query complexity of graph parameter estimation problems. In particular, our technique decouples the lower bound arguments from the representation of the graph, allowing it to work with any query type. We illustrate our technique by providing new simpler proofs of previously known tight lower bounds for the query complexity of several graph problems: Estimating the number of edges in a graph, sampling edges from an almost-uniform distribution, estimating the number of triangles (and more generally, r-cliques) in a graph, and estimating the moments of the degree distribution of a graph. We also prove new lower bounds for estimating the edge connectivity of a graph and estimating the number of instances of any fixed subgraph in a graph. We show that the lower bounds for estimating the number of triangles and edge connectivity also hold in a strictly stronger computational model that allows access to uniformly random edge samples.
AB - In a celebrated work, Blais, Brody, and Matulef [7] developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower bounds as well as simplified analyses of known lower bounds. Here, we take a further step in generalizing the methodology of [7] to analyze the query complexity of graph parameter estimation problems. In particular, our technique decouples the lower bound arguments from the representation of the graph, allowing it to work with any query type. We illustrate our technique by providing new simpler proofs of previously known tight lower bounds for the query complexity of several graph problems: Estimating the number of edges in a graph, sampling edges from an almost-uniform distribution, estimating the number of triangles (and more generally, r-cliques) in a graph, and estimating the moments of the degree distribution of a graph. We also prove new lower bounds for estimating the edge connectivity of a graph and estimating the number of instances of any fixed subgraph in a graph. We show that the lower bounds for estimating the number of triangles and edge connectivity also hold in a strictly stronger computational model that allows access to uniformly random edge samples.
KW - Communication Complexity
KW - Lower Bounds
KW - Sublinear Graph Parameter Estimation
UR - http://www.scopus.com/inward/record.url?scp=85052462801&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.APPROX-RANDOM.2018.11
DO - 10.4230/LIPIcs.APPROX-RANDOM.2018.11
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AN - SCOPUS:85052462801
SN - 9783959770859
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018
A2 - Blais, Eric
A2 - Rolim, Jose D. P.
A2 - Steurer, David
A2 - Jansen, Klaus
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018
Y2 - 20 August 2018 through 22 August 2018
ER -