Lectures

Lecture # Content Reference
1 Introduction to communication complexity, protocol partition and tiling, clique vs independent set. KN97 (§ 1.1, 1.2, 2.2, 2.3), Juk12 (§ 3.2, 4.4)
2 Fooling set and rectangle size bound, rank bound, comparison of two techniques, non-determinism. KN97 (§ 1.3, 1.4, 2.1, 2.5), DHS96
3 More on non-determinism, $P = NP \cap coNP$, Separation of $P$ and $NP \cap coNP$, $UP$, Decision tree and composed functions. KN97 (§ 2.3 - 2.5), Juk11 (§ 13.4), GPW15
4 Simulation theorem (I): Hitting distribution for $GH$, The simulation algorithm. GPW15, CKLM17
5 Simulation theorem (II): Thickness and its properties, The simulation algorithm. GPW15, CKLM17
6 Randomization: Zero-error, one-sided error, $EQ$ function and separations, Private coin vs public coin. KN97 (§ 3.1 - 3.3)
7 Protocol for $GT, DISJ_{nk}$, Distributional complexity, Yao’s minimax principle. KN97 (§ 3.4), HW07
8 Discrepancy: lower bound for $IP_n, GT_n$; Disjointness under product distribution. KN97 (§ 3.5), CP10, BW16
9 Disjointness under product distribution: Lower bound and upper bound. CP10, BFS86
10 Corruption bound, Razborov’s hard distribution for $DISJ_n$, Index function. KN97 (§ 4.6), CP10, GW16
11 Information theory primer, Index function lower bound, Information complexity. RY18 (§ 6.1 - 6.4), BJKS04, JKS03
12 Direct sum of information complexity, Lower bound for $DISJ_n$. RY18 (§ 6.1 - 6.4), BJKS04, JKS03, Bra17, BR11
13 Asymmetric communication complexity, Richness method, Index function and lopsided $DISJ$, Application in data-structure. KN97 (§ 4.3), MNWS98
14 Lecture by Jakob Nordström (I). Proof systems, Proof complexity and communication complexity, (Critical) block sensitivity. HN12, Notes
15 Lecture by Jakob Nordström (II). Communication complexity of lifted search problem. HN12, Notes
Sagnik Mukhopadhyay
Sagnik Mukhopadhyay
Post-doctoral Researcher

My research interests include complexity theory and distributed graph algorithms.