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- Dimitris Achlioptas, Amin Coja-Oghlan
- 2008 49th Annual IEEE Symposium on Foundations of…
- 2008

For many random constraint satisfaction problems, by now there exist asymptotically tight estimates of the largest constraint density for which solutions exist. At the same time, for many of these problems, all known polynomial-time algorithms stop finding solutions at much smaller densities. For example, it is well-known that it is easy to color a random… (More)

- Amin Coja-Oghlan
- Electronic Colloquium on Computational Complexity
- 2006

In this paper we study the use of spectral techniques for graph partitioning. Let G = (V, E) be a graph whose vertex set has a " latent " partition V1,. .. , V k. Moreover, consider a " density matrix " E = (Evw)v,w∈V such that for v ∈ Vi and w ∈ Vj the entry Evw is the fraction of all possible Vi-Vj-edges that are actually present in G. We show that on… (More)

- Amin Coja-Oghlan, Andreas Goerdt, André Lanka
- Combinatorics, Probability & Computing
- 2004

- Noga Alon, Amin Coja-Oghlan, Hiêp Hàn, Mihyun Kang, Vojtech Rödl, Mathias Schacht
- SIAM J. Comput.
- 2007

We deal with two intimately related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to measure how much a given graph " resembles " a random one. Moreover , a regular partition approximates a given graph by a bounded number of quasi-random graphs. Regarding quasi-randomness, we present a new spectral… (More)

- Amin Coja-Oghlan, Anusch Taraz
- Random Struct. Algorithms
- 2004

- Amin Coja-Oghlan
- Random Struct. Algorithms
- 2005

The minimum bisection problem is to partition the vertices of a graph into two classes of equal size so as to minimize the number of crossing edges. The problem is NP-hard in the worst case. In this paper we analyze a spectral heuristic for the minimum bisection problem on random graphs <i>G<inf>n</inf></i>(<i>p,p'</i>), which are made up as follows.… (More)

- Amin Coja-Oghlan, Cristopher Moore, Vishal Sanwalani
- ICALP
- 2003

- Amin Coja-Oghlan
- SIAM J. Comput.
- 2009

Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of Φ with high probability for constraint densities m/n < (1 − ε k)2 k ln(k)/k, where ε k → 0. Previously no efficient algorithm was known to find solutions with non-vanishing probability beyond m/n… (More)

- Amin Coja-Oghlan, Colin Cooper, Alan M. Frieze
- SODA
- 2009

Let A be a 0/1 matrix of size m × n, and let p be the density of A (i.e., the number of ones divided by m · n). We show that A can be approximated in the cut norm within ε · mnp by a sum of cut matrices (of rank 1), where the number of summands is independent of the size m·n of A, provided that A satisfies a certain boundedness condition. This decomposition… (More)

- Amin Coja-Oghlan
- SODA
- 2011

Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-constructive arguments show that Φ is satisfiable for clause/variable ratios m/n ≤ r k ∼ 2 k ln 2 with high probability. Yet no efficient algorithm is know to find a satisfying assignment for densities as low as m/n ∼ r k · ln(k)/k with a non-vanishing probability. In… (More)