Pointer chasing via triangular discrimination

We prove an essentially sharp Ω̃(n/k) lower bound on the k-round distributional complexity of the k-step pointer chasing problem under the uniform distribution, when Bob speaks first. This is an improvement over Nisan and Wigderson’s Ω̃(n/k2) lower bound. A key part of the proof is using triangular discrimination instead of total variation distance; this idea may be useful elsewhere.

[1]  Peter Bro Miltersen,et al.  On data structures and asymmetric communication complexity , 1994, STOC '95.

[2]  Zvi Galil,et al.  Lower bounds on communication complexity , 1984, STOC '84.

[3]  Gady Kozma,et al.  Disorder, entropy and harmonic functions , 2011, 1111.4853.

[4]  Flemming Topsøe,et al.  Some inequalities for information divergence and related measures of discrimination , 2000, IEEE Trans. Inf. Theory.

[5]  Jaikumar Radhakrishnan,et al.  The Communication Complexity of Pointer Chasing , 2001, J. Comput. Syst. Sci..

[6]  Danupon Nanongkai,et al.  A tight unconditional lower bound on distributed randomwalk computation , 2011, PODC '11.

[7]  Jirí Sgall,et al.  Some bounds on multiparty communication complexity of pointer jumping , 1998, computational complexity.

[8]  Noam Nisan,et al.  Rounds in communication complexity revisited , 1991, STOC '91.

[9]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[10]  Subhash Khot.  On the power of unique 2-prover 1-round games , 2002, STOC '02.

[11]  Venkatesan Guruswami,et al.  Superlinear Lower Bounds for Multipass Graph Processing , 2013, Computational Complexity Conference.

[12]  Imre Csiszár,et al.  Information Theory and Statistics: A Tutorial , 2004, Found. Trends Commun. Inf. Theory.

[13]  E. Kushilevitz,et al.  Communication Complexity: Basics , 1996 .

[14]  Alexander A. Razborov,et al.  On the Distributional Complexity of Disjointness , 1992, Theor. Comput. Sci..

[15]  Xi Chen,et al.  How to Compress Interactive Communication , 2013, SIAM J. Comput..

[16]  Hartmut Klauck,et al.  Interaction in Quantum Communication , 2006, IEEE Transactions on Information Theory.

[17]  Mark Braverman,et al.  Direct Products in Communication Complexity , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[18]  Hartmut Klauck,et al.  On quantum and probabilistic communication: Las Vegas and one-way protocols , 2000, STOC '00.

[19]  Ran Raz,et al.  A Counterexample to Strong Parallel Repetition , 2008, FOCS.

[20]  Mihalis Yannakakis,et al.  On monotone formulae with restricted depth , 1984, STOC '84.

[21]  Srinivasan Venkatesh,et al.  Lower bounds for predecessor searching in the cell probe model , 2003, J. Comput. Syst. Sci..