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Electronic Colloquium on Computational Complexity

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All reports by Author Nader Bshouty:

TR18-053 | 19th March 2018
Nader Bshouty

Lower Bound for Non-Adaptive Estimate the Number of Defective Items

We prove that to estimate within a constant factor the number of defective items in a non-adaptive group testing algorithm we need at least $\tilde\Omega((\log n)(\log(1/\delta)))$ tests. This solves the open problem posed by Damaschke and Sheikh Muhammad.

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TR16-083 | 23rd May 2016
Nader Bshouty

Derandomizing Chernoff Bound with Union Bound with an Application to $k$-wise Independent Sets

Derandomization of Chernoff bound with union bound is already proven in many papers.
We here give another explicit version of it that obtains a construction of size
that is arbitrary close to the probabilistic nonconstructive size.

We apply this to give a new simple polynomial time constructions of
almost $k$-wise ... more >>>

TR15-006 | 6th January 2015
Nader Bshouty

Dense Testers: Almost Linear Time and Locally Explicit Constructions

We develop a new notion called {\it $(1-\epsilon)$-tester for a
set $M$ of functions} $f:A\to C$. A $(1-\epsilon)$-tester
for $M$ maps each element $a\in A$ to a finite number of
elements $B_a=\{b_1,\ldots,b_t\}\subset B$ in a smaller
sub-domain $B\subset A$ where for every $f\in M$ if
$f(a)\not=0$ then $f(b)\not=0$ for at ... more >>>

TR13-012 | 16th January 2013
Hasan Abasi, Nader Bshouty

A Simple Algorithm for Undirected Hamiltonicity

We develop a new algebraic technique that gives a simple randomized algorithm for the simple $k$-path problem with the same complexity $O^*(1.657^k)$ as in [A. Bj\"orklund. Determinant Sums for Undirected Hamiltonicity. FOCS 2010, pp. 173--182, (2010). A. Bj\"orklund, T. Husfeldt, P. Kaski, M. Koivisto. Narrow sieves for parameterized paths and ... more >>>

TR13-011 | 10th January 2013
Nader Bshouty

Multilinear Complexity is Equivalent to Optimal Tester Size

In this paper we first show that Tester for an $F$-algebra $A$
and multilinear forms (see Testers and their Applications ECCC 2012) is equivalent to multilinear
algorithm for the product of elements in $A$
(see Algebraic
complexity theory. vol. 315, Springer-Verlag). Our
result is constructive in deterministic polynomial time. ... more >>>

TR12-011 | 7th February 2012
Nader Bshouty

Testers and their Applications

We develop a new notion called {\it tester of a class $\cM$ of
functions} $f:\cA\to \cC$ that maps the elements $\bfa\in \cA$ in
the domain $\cA$ of the function to a finite number (the size of
the tester) of elements $\bfb_1,\ldots,\bfb_t$ in a smaller
sub-domain $\cB\subset \cA$ where the property ... more >>>

TR11-124 | 15th September 2011
Nader Bshouty, Hanna Mazzawi

Algorithms for the Coin Weighing Problems with the Presence of Noise

The coin weighing problem is the following: Given $n$ coins for which $m$ of them are counterfeit with the same weight. The problem is to detect the counterfeit coins with minimal number of weighings. This problem has many applications in compressed sensing, multiple access adder channels, etc. The problem was ... more >>>

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