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Electronic Colloquium on Computational Complexity

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All reports by Author Rajeev Motwani:

TR06-156 | 7th December 2006
Tomas Feder, Rajeev Motwani

Finding large cycles in Hamiltonian graphs

We show how to find in Hamiltonian graphs a cycle of length
$n^{\Omega(1/\log\log n)}$. This is a consequence of a more general
result in which we show that if $G$ has maximum degree $d$ and has a
cycle with $k$ vertices (or a 3-cyclable minor $H$ with $k$ vertices),
then ... more >>>

TR06-041 | 6th March 2006
Tomas Feder, Rajeev Motwani, An Zhu

k-connected spanning subgraphs of low degree

We consider the problem of finding a $k$-vertex ($k$-edge)
connected spanning subgraph $K$ of a given $n$-vertex graph $G$
while minimizing the maximum degree $d$ in $K$. We give a
polynomial time algorithm for fixed $k$ that achieves an $O(\log
n)$-approximation. The only known previous polynomial algorithms
achieved degree $d+1$ ... more >>>

TR06-040 | 6th March 2006
Tomas Feder, Gagan Aggarwal, Rajeev Motwani, An Zhu

Channel assignment in wireless networks and classification of minimum graph homomorphism

We study the problem of assigning different communication channels to
acces points in a wireless Local Area Network. Each access point will
be assigned a specific radio frequency channel. Since channels with
similar frequencies interfere, it is desirable to assign far apart
channels (frequencies) to nearby access points. Our goal ... more >>>

TR98-008 | 15th January 1998
Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, Mario Szegedy

Proof verification and the hardness of approximation problems.

We show that every language in NP has a probablistic verifier
that checks membership proofs for it using
logarithmic number of random bits and by examining a
<em> constant </em> number of bits in the proof.
If a string is in the language, then there exists a proof ... more >>>

TR95-023 | 16th May 1995
Sanjeev Khanna, Rajeev Motwani, Madhu Sudan, Umesh Vazirani

On Syntactic versus Computational views of Approximability

We attempt to reconcile the two distinct views of approximation
classes: syntactic and computational.
Syntactic classes such as MAX SNP allow for clean complexity-theoretic
results and natural complete problems, while computational classes such
as APX allow us to work with problems whose approximability is
well-understood. Our results give a computational ... more >>>

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