1 research outputs found
Popular conjectures imply strong lower bounds for dynamic problems
We consider several well-studied problems in dynamic algorithms and prove
that sufficient progress on any of them would imply a breakthrough on one of
five major open problems in the theory of algorithms:
1. Is the 3SUM problem on numbers in time for some
?
2. Can one determine the satisfiability of a CNF formula on variables in
time for some ?
3. Is the All Pairs Shortest Paths problem for graphs on vertices in
time for some ?
4. Is there a linear time algorithm that detects whether a given graph
contains a triangle?
5. Is there an time combinatorial algorithm for Boolean matrix multiplication?
The problems we consider include dynamic versions of bipartite perfect
matching, bipartite maximum weight matching, single source reachability, single
source shortest paths, strong connectivity, subgraph connectivity, diameter
approximation and some nongraph problems such as Pagh's problem defined in a
recent paper by Patrascu [STOC 2010]