Improved Lower Bounds on the Randomized Complexity of Graph Properties

We prove a lower bound of (n4/3 log1/3 n) on the randomized decision tree complexity of any nontrivial monotone n-vertex graph property, and of any nontrivial monotone bipartite graph property with bipartitions of size n. This improves the previous best bound of (n4/3) due to Hajnal [Haj91]. Our proof works by improving a graph packing lemma used in earlier work, and this improvement in turn stems from a novel probabilistic analysis. Graph packing being a well-studied subject in its own right, our improved packing lemma and the probabilistic technique used to prove it may be of independent interest.

• Type: Conference
• Year: 2001
• Where: ICALP
• Authors: Amit Chakrabarti, Subhash Khot
• Keywords: Graph Packing, Graph Property, ICALP 2001, Nontrivial Monotone, Programming Languages