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Electronic Colloquium on Computational Complexity

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All reports by Author Uriel Feige:

TR14-110 | 19th August 2014
Uriel Feige, Shlomo Jozeph

Separation between Estimation and Approximation

We show (under standard assumptions) that there are NP optimization problems for which estimation is easier than approximation. Namely, one can estimate the value of the optimal solution within a ratio of $\rho$, but it is difficult to find a solution whose value is within $\rho$ of optimal.
As an ... more >>>

TR14-103 | 8th August 2014
Uriel Feige, Michal Feldman, Nicole Immorlica, Rani Izsak, Lucier Brendan, Vasilis Syrgkanis

A Unifying Hierarchy of Valuations with Complements and Substitutes

We introduce a new hierarchy over monotone set functions, that we refer to as $MPH$ (Maximum over Positive Hypergraphs).
Levels of the hierarchy correspond to the degree of complementarity in a given function.
The highest level of the hierarchy, $MPH$-$m$ (where $m$ is the total number of items) captures all ... more >>>

TR13-095 | 24th June 2013
Uriel Feige, Rani Izsak

Welfare Maximization and the Supermodular Degree

Given a set of items and a collection of players, each with a nonnegative monotone valuation set function over the items,
the welfare maximization problem requires that every item be allocated to exactly one player,
and one wishes to maximize the sum of values obtained by the players,
as computed ... more >>>

TR07-043 | 7th May 2007
Uriel Feige, Guy Kindler, Ryan O'Donnell

Understanding Parallel Repetition Requires Understanding Foams

Motivated by the study of Parallel Repetition and also by the Unique
Games Conjecture, we investigate the value of the ``Odd Cycle Games''
under parallel repetition. Using tools from discrete harmonic
analysis, we show that after $d$ rounds on the cycle of length $m$,
the value of the game is ... more >>>

TR06-043 | 22nd March 2006
Eran Ofek, Uriel Feige

Random 3CNF formulas elude the Lovasz theta function

Let $\phi$ be a 3CNF formula with n variables and m clauses. A
simple nonconstructive argument shows that when m is
sufficiently large compared to n, most 3CNF formulas are not
satisfiable. It is an open question whether there is an efficient
refutation algorithm that for most such formulas proves ... more >>>

TR05-050 | 18th April 2005
Uriel Feige, Eran Ofek

Finding a Maximum Independent Set in a Sparse Random Graph

Revisions: 1

We consider the problem of finding a maximum independent set in a
random graph. The random graph $G$ is modelled as follows. Every
edge is included independently with probability $\frac{d}{n}$, where
$d$ is some sufficiently large constant. Thereafter, for some
constant $\alpha$, a subset $I$ of $\alpha n$ vertices is ... more >>>

TR04-119 | 8th December 2004
Uriel Feige, Daniel Reichman

On The Hardness of Approximating Max-Satisfy

Max-Satisfy is the problem of finding an assignment that satisfies
the maximum number of equations in a system of linear equations
over $\mathbb{Q}$. We prove that unless NP$\subseteq $BPP there is no
polynomial time algorithm for the problem achieving an
approximation ratio of $1/n^{1-\epsilon}$, where $n$ is the number
of ... more >>>

TR00-043 | 21st June 2000
Uriel Feige, Marek Karpinski, Michael Langberg

A Note on Approximating MAX-BISECTION on Regular Graphs

We design a $0.795$ approximation algorithm for the Max-Bisection problem
restricted to regular graphs. In the case of three regular graphs our
results imply an approximation ratio of $0.834$.

more >>>

TR00-021 | 19th April 2000
Uriel Feige, Marek Karpinski, Michael Langberg

Improved Approximation of MAX-CUT on Graphs of Bounded Degree

We analyze the addition of a simple local improvement step to various known
randomized approximation algorithms.
Let $\alpha \simeq 0.87856$ denote the best approximation ratio currently
known for the Max Cut problem on general graphs~\cite{GW95}.
We consider a semidefinite relaxation of the Max Cut problem,
round it using the ... more >>>

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