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Electronic Colloquium on Computational Complexity

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All reports by Author Shay Moran:

TR17-085 | 4th May 2017
Daniel Kane, Shachar Lovett, Shay Moran, Jiapeng Zhang

Active classification with comparison queries

We study an extension of active learning in which the learning algorithm may ask the annotator to compare the distances of two examples from the boundary of their label-class. For example, in a recommendation system application (say for restaurants), the annotator may be asked whether she liked or disliked a ... more >>>

TR17-082 | 4th May 2017
Daniel Kane, Shachar Lovett, Shay Moran

Near-optimal linear decision trees for k-SUM and related problems

We construct near optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry.
For example, for any constant $k$, we construct linear decision trees that solve the $k$-SUM problem on $n$ elements using $O(n \log^2 n)$ linear queries.
Moreover, the queries we use are comparison ... more >>>

TR15-189 | 25th November 2015
Shay Moran, Cyrus Rashtchian

Shattered Sets and the Hilbert Function

Revisions: 1

We study complexity measures on subsets of the boolean hypercube and exhibit connections between algebra (the Hilbert function) and combinatorics (VC theory). These connections yield results in both directions. Our main complexity-theoretic result proves that most linear program feasibility problems cannot be computed by polynomial-sized constant-depth circuits. Moreover, our result ... more >>>

TR15-040 | 24th March 2015
Shay Moran, Amir Yehudayoff

Proper PAC learning is compressing

Revisions: 1

We prove that proper PAC learnability implies compression. Namely, if a concept $C \subseteq \Sigma^X$ is properly PAC learnable with $d$ samples, then $C$ has a sample compression scheme of size $2^{O(d)}$.
In particular, every boolean concept class with constant VC dimension has a sample compression scheme of constant size. ... more >>>

TR15-025 | 22nd February 2015
Shay Moran, Amir Shpilka, Avi Wigderson, Amir Yehudayoff

Teaching and compressing for low VC-dimension

In this work we study the quantitative relation between VC-dimension and two other basic parameters related to learning and teaching. We present relatively efficient constructions of {\em sample compression schemes} and
for classes of low VC-dimension. Let $C$ be a finite boolean concept class of VC-dimension $d$. Set $k ... more >>>

TR14-135 | 23rd October 2014
Noga Alon, Shay Moran, Amir Yehudayoff

Sign rank, VC dimension and spectral gaps

Revisions: 2

We study the maximum possible sign rank of $N \times N$ sign matrices with a given VC dimension $d$. For $d=1$, this maximum is $3$. For $d=2$, this maximum is $\tilde{\Theta}(N^{1/2})$. Similar (slightly less accurate) statements hold for $d>2$ as well. We discuss the tightness of our methods, and describe ... more >>>

TR14-101 | 8th August 2014
Balthazar Bauer, Shay Moran, Amir Yehudayoff

Internal compression of protocols to entropy

Revisions: 1

We study internal compression of communication protocols
to their internal entropy, which is the entropy of the transcript from the players' perspective.
We first show that errorless compression to the internal entropy
(and hence to the internal information) is impossible.
We then provide two internal compression schemes with error.
One ... more >>>

TR14-046 | 8th April 2014
Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

Approximate Nonnegative Rank is Equivalent to the Smooth Rectangle Bound

We consider two known lower bounds on randomized communication complexity: The smooth rectangle bound and the logarithm of the approximate non-negative rank. Our main result is that they are the same up to a multiplicative constant and a small additive term.
The logarithm of the nonnegative rank is known to ... more >>>

TR13-106 | 29th July 2013
Shay Moran, Amir Yehudayoff

A note on average-case sorting

Revisions: 2

This note studies the average-case comparison-complexity of sorting n elements when there is a known distribution on inputs and the goal is to minimize
the expected number of comparisons. We generalize Fredman's algorithm which
is a variant of insertion sort and provide a basically tight upper bound: If \mu is
more >>>

TR13-079 | 2nd June 2013
Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

Direct Sum Fails for Zero Error Average Communication

We show that in the model of zero error communication complexity, direct sum fails for average communication complexity as well as for external information cost. Our example also refutes a version of a conjecture by Braverman et al. that in the zero error case amortized communication complexity equals external information ... more >>>

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