Electronic Colloquium on Computational Complexity

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All reports by Author Sanjeev Khanna:

TR07-113 | 15th November 2007
Matthew Andrews, Julia Chuzhoy, Venkatesan Guruswami, Sanjeev Khanna, Kunal Talwar, Lisa Zhang

Inapproximability of edge-disjoint paths and low congestion routing on undirected graphs

In the undirected Edge-Disjoint Paths problem with Congestion
(EDPwC), we are given an undirected graph with $V$ nodes, a set of
terminal pairs and an integer $c$. The objective is to route as many
terminal pairs as possible, subject to the constraint that at most
$c$ demands can be routed ... more >>>

TR06-109 | 29th August 2006
Julia Chuzhoy, Sanjeev Khanna

Hardness of Directed Routing with Congestion

Given a graph G and a collection of source-sink pairs in G, what is the least integer c such that each source can be connected by a path to its sink, with at most c paths going through an edge? This is known as the congestion minimization problem, and the ... more >>>

TR03-038 | 15th May 2003
Julia Chuzhoy, Sudipto Guha, Sanjeev Khanna, Seffi Naor

Asymmetric k-center is log^*n-hard to Approximate

We show that the asymmetric $k$-center problem is
$\Omega(\log^* n)$-hard to approximate unless
${\rm NP} \subseteq {\rm DTIME}(n^{poly(\log \log n)})$.
Since an $O(\log^* n)$-approximation algorithm is known
for this problem, this essentially resolves the approximability
of this problem. This is the first natural problem
whose approximability threshold does not polynomially ... more >>>

TR03-032 | 16th April 2003
Andreas Björklund, Thore Husfeldt, Sanjeev Khanna

Approximating Longest Directed Path

We investigate the hardness of approximating the longest path and
the longest cycle in directed graphs on $n$ vertices. We show that
neither of these two problems can be polynomial time approximated
within $n^{1-\epsilon}$ for any $\epsilon>0$ unless
$\text{P}=\text{NP}$. In particular, the result holds for
more >>>

TR01-065 | 10th August 2001
Chandra Chekuri, Sanjeev Khanna

Approximation Schemes for Preemptive Weighted Flow Time

We present the first approximation schemes for minimizing weighted flow time
on a single machine with preemption. Our first result is an algorithm that
computes a $(1+\eps)$-approximate solution for any instance of weighted flow
time in $O(n^{O(\ln W \ln P/\eps^3)})$ time; here $P$ is the ratio ... more >>>

TR00-073 | 28th August 2000
Venkatesan Guruswami, Sanjeev Khanna

On the Hardness of 4-coloring a 3-colorable Graph

We give a new proof showing that it is NP-hard to color a 3-colorable
graph using just four colors. This result is already known (Khanna,
Linial, Safra 1992), but our proof is novel as it does not rely on
the PCP theorem, while the earlier one does. This ... more >>>

TR96-064 | 11th December 1996
Sanjeev Khanna, Madhu Sudan, Luca Trevisan

Constraint satisfaction: The approximability of minimization problems.

This paper continues the work initiated by Creignou [Cre95] and
Khanna, Sudan and Williamson [KSW96] who classify maximization
problems derived from boolean constraint satisfaction. Here we
study the approximability of {\em minimization} problems derived
thence. A problem in this framework is characterized by a
collection F ... more >>>

TR96-062 | 3rd December 1996
Sanjeev Khanna, Madhu Sudan, David P. Williamson

A Complete Characterization of the Approximability of Maximization Problems Derived from Boolean Constraint Satisfaction

In this paper we study the approximability of boolean constraint
satisfaction problems. A problem in this class consists of some
collection of ``constraints'' (i.e., functions
$f:\{0,1\}^k \rightarrow \{0,1\}$); an instance of a problem is a set
of constraints applied to specified subsets of $n$ boolean
variables. Schaefer earlier ... more >>>

TR96-028 | 9th April 1996
Sanjeev Khanna, Madhu Sudan

The Optimization Complexity of Constraint Satisfaction Problems

In 1978, Schaefer considered a subclass of languages in
NP and proved a ``dichotomy theorem'' for this class. The subclass
considered were problems expressible as ``constraint satisfaction
problems'', and the ``dichotomy theorem'' showed that every language in
this class is either in P, or is NP-hard. This result is in ... 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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