Placing regenerators in optical networks to satisfy multiple sets of requests
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
On the hardness and inapproximability of optimization problems on power law graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Recoverable values for independent sets
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Vertex cover in graphs with locally few colors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On LP-based approximability for strict CSPs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of finding independent sets in bounded degree (hyper)graphs of low chromatic number
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
SubMAP: aligning metabolic pathways with subnetwork mappings
RECOMB'10 Proceedings of the 14th Annual international conference on Research in Computational Molecular Biology
Approximability of economic equilibrium for housing markets with duplicate houses
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
On k-column sparse packing programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
New techniques for approximating optimal substructure problems in power-law graphs
Theoretical Computer Science
Vertex cover in graphs with locally few colors
Information and Computation
SDP-based algorithms for maximum independent set problems on hypergraphs
Theoretical Computer Science
Placing regenerators in optical networks to satisfy multiple sets of requests
IEEE/ACM Transactions on Networking (TON)
Complexity of approximating CSP with balance / hard constraints
Proceedings of the 5th conference on Innovations in theoretical computer science
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We study the inapproximability of Vertex Cover and Independent Set on degree $d$ graphs. We prove that: \begin{itemize} \item Vertex Cover is Unique Games-hard to approximate to within a factor $2 - (2+o_d(1)) \frac{ \log\log d}{ \log d}$. This exactly matches the algorithmic result of Halperin \cite{halperin02improved} up to the $o_d(1)$ term. \item Independent Set is Unique Games-hard to approximate to within a factor $O(\frac{d}{\log^2 d})$. This improves the $\frac{d}{\log^{O(1)}(d)}$ Unique Games hardness result of Samorodnitsky and Trevisan \cite{samorodnitsky06gowers}. Additionally, our result does not rely on the construction of a query efficient PCP as in \cite{samorodnitsky06gowers}. \end{itemize}