TY - GEN
T1 - Almost optimal super-constant-pass streaming lower bounds for reachability
AU - Chen, Lijie
AU - Kol, Gillat
AU - Paramonov, Dmitry
AU - Saxena, Raghuvansh R.
AU - Song, Zhao
AU - Yu, Huacheng
N1 - Funding Information:
Lijie Chen is supported by an IBM Fellowship. Zhao Song is supported in part by Ma Huateng Foundation, Schmidt Foundation, Simons Foundation, NSF, DARPA/SRC, Google and Amazon AWS.
Publisher Copyright:
© 2021 ACM.
PY - 2021/6/15
Y1 - 2021/6/15
N2 - We give an almost quadratic n2-o(1) lower bound on the space consumption of any o(?logn)-pass streaming algorithm solving the (directed) s-t reachability problem. This means that any such algorithm must essentially store the entire graph. As corollaries, we obtain almost quadratic space lower bounds for additional fundamental problems, including maximum matching, shortest path, matrix rank, and linear programming. Our main technical contribution is the definition and construction of set hiding graphs, that may be of independent interest: we give a general way of encoding a set S ? [k] as a directed graph with n = k 1 + o( 1 ) vertices, such that deciding whether i e S boils down to deciding if ti is reachable from si, for a specific pair of vertices (si,ti) in the graph. Furthermore, we prove that our graph "hides"S, in the sense that no low-space streaming algorithm with a small number of passes can learn (almost) anything about S.
AB - We give an almost quadratic n2-o(1) lower bound on the space consumption of any o(?logn)-pass streaming algorithm solving the (directed) s-t reachability problem. This means that any such algorithm must essentially store the entire graph. As corollaries, we obtain almost quadratic space lower bounds for additional fundamental problems, including maximum matching, shortest path, matrix rank, and linear programming. Our main technical contribution is the definition and construction of set hiding graphs, that may be of independent interest: we give a general way of encoding a set S ? [k] as a directed graph with n = k 1 + o( 1 ) vertices, such that deciding whether i e S boils down to deciding if ti is reachable from si, for a specific pair of vertices (si,ti) in the graph. Furthermore, we prove that our graph "hides"S, in the sense that no low-space streaming algorithm with a small number of passes can learn (almost) anything about S.
KW - Communication Complexity
KW - Graph Streaming
KW - Lower Bounds
UR - http://www.scopus.com/inward/record.url?scp=85108144807&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85108144807&partnerID=8YFLogxK
U2 - 10.1145/3406325.3451038
DO - 10.1145/3406325.3451038
M3 - Conference contribution
AN - SCOPUS:85108144807
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 570
EP - 583
BT - STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
A2 - Khuller, Samir
A2 - Williams, Virginia Vassilevska
PB - Association for Computing Machinery
T2 - 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Y2 - 21 June 2021 through 25 June 2021
ER -