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Electronic Colloquium on Computational Complexity

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All reports by Author Kasper Green Larsen:

TR23-002 | 5th January 2023
Noga Alon, Olivier Bousquet, Kasper Green Larsen, Shay Moran, Shlomo Moran

Diagonalization Games

Revisions: 2

We study several variants of a combinatorial game which is based on Cantor's diagonal argument. The game is between two players called Kronecker and Cantor. The names of the players are motivated by the known fact that Leopold Kronecker did not appreciate Georg Cantor's arguments about the infinite, and even ... more >>>

TR19-055 | 9th April 2019
Kasper Green Larsen, Tal Malkin, Omri Weinstein, Kevin Yeo

Lower Bounds for Oblivious Near-Neighbor Search

We prove an $\Omega(d \lg n/ (\lg\lg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $\mathit{oblivious}$ approximate-near-neighbor search (ANN) over the $d$-dimensional Hamming cube. For the natural setting of $d = \Theta(\log n)$, our result implies an $\tilde{\Omega}(\lg^2 n)$ lower bound, which is a quadratic improvement over the ... more >>>

TR18-109 | 29th May 2018
Kasper Green Larsen, Jesper Buus Nielsen

Yes, There is an Oblivious RAM Lower Bound!

An Oblivious RAM (ORAM) introduced by Goldreich and Ostrovsky
[JACM'96] is a (possibly randomized) RAM, for which the memory access
pattern reveals no information about the operations
performed. The main performance metric of an ORAM is the bandwidth
overhead, i.e., the multiplicative factor extra memory blocks that must be
accessed ... more >>>

TR17-047 | 10th March 2017
Kasper Green Larsen, Omri Weinstein, Huacheng Yu

Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds

This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic \emph{boolean} (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds.

We introduce a new method for proving dynamic cell probe lower bounds and use it to prove a $\tilde{\Omega}(\log^{1.5} ... more >>>

TR12-087 | 4th July 2012
Peyman Afshani, Manindra Agrawal, Doerr Benjamin, Winzen Carola, Kasper Green Larsen, Kurt Mehlhorn

The Deterministic and Randomized Query Complexity of a Simple Guessing Game

Revisions: 1

We study the $\leadingones$ game, a Mastermind-type guessing game first
regarded as a test case in the complexity theory of randomized search
heuristics. The first player, Carole, secretly chooses a string $z \in \{0,1\}^n$ and a
permutation $\pi$ of $[n]$.
The goal of the second player, Paul, is to ... more >>>

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