Electronic Colloquium on Computational Complexity
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Reports tagged with Approximation algorithm:
TR01-084 | 1st October 2001
Gerhard J. Woeginger

When does a dynamic programming formulation guarantee the existence of an FPTAS?

We derive results of the following flavor:
If a combinatorial optimization problem can be formulated via a dynamic
program of a certain structure and if the involved cost and transition
functions satisfy certain arithmetical and structural conditions, then
the optimization problem automatically possesses a fully polynomial time
approximation scheme (FPTAS).

... more >>>

TR02-025 | 26th April 2002
Wenceslas Fernandez de la Vega, Marek Karpinski, Claire Kenyon, Yuval Rabani

Polynomial Time Approximation Schemes for Metric Min-Sum Clustering

We give polynomial time approximation schemes for the problem
of partitioning an input set of n points into a fixed number
k of clusters so as to minimize the sum over all clusters of
the total pairwise distances in a cluster. Our algorithms work
for arbitrary metric spaces as well ... more >>>

TR02-054 | 5th September 2002
Detlef Sieling

Minimization of Decision Trees is Hard to Approximate

Decision trees are representations of discrete functions with widespread applications in, e.g., complexity theory and data mining and exploration. In these areas it is important to obtain decision trees of small size. The minimization problem for decision trees is known to be NP-hard. In this paper the problem is shown ... more >>>

TR04-050 | 13th June 2004
Michelle Effros, Leonard J. Schulman

Deterministic clustering with data nets

We consider the $K$-clustering problem with the $\ell_2^2$
distortion measure, also known as the problem of optimal
fixed-rate vector quantizer design. We provide a deterministic
approximation algorithm which works for all dimensions $d$ and
which, given a data set of size $n$, computes in time
more >>>

TR04-084 | 28th September 2004
George Karakostas

A better approximation ratio for the Vertex Cover problem

We reduce the approximation factor for Vertex Cover to $2-\Theta(1/\sqrt{logn})$
(instead of the previous $2-\Theta(loglogn/logn})$, obtained by Bar-Yehuda and Even,
and by Monien and Speckenmeyer in 1985. The improvement of the vanishing
factor comes as an application of the recent results of Arora, Rao, and Vazirani
that improved ... more >>>

TR06-007 | 23rd November 2005
MohammadTaghi Hajiaghayi, Guy Kortsarz, Mohammad R. Salavatipour

Approximating Buy-at-Bulk $k$-Steiner trees

In the buy-at-bulk $k$-Steiner tree (or rent-or-buy
$k$-Steiner tree) problem we are given a graph $G(V,E)$ with a set
of terminals $T\subseteq V$ including a particular vertex $s$ called
the root, and an integer $k\leq |T|$. There are two cost functions
on the edges of $G$, a buy cost $b:E\longrightarrow ... more >>>

TR06-063 | 1st May 2006
Moses Charikar, Konstantin Makarychev, Yury Makarychev

Approximation Algorithm for the Max k-CSP Problem

We present a c.k/2^k approximation algorithm for the Max k-CSP problem (where c > 0.44 is an absolute constant). This result improves the previously best known algorithm by Hast, which has an approximation guarantee of Omega(k/(2^k log k)). Our approximation guarantee matches the upper bound of Samorodnitsky and Trevisan up ... more >>>

TR06-064 | 1st May 2006
Moses Charikar, Konstantin Makarychev, Yury Makarychev

Note on MAX 2SAT

In this note we present an approximation algorithm for MAX 2SAT that given a (1 - epsilon) satisfiable instance finds an assignment of variables satisfying a 1 - O(sqrt{epsilon}) fraction of all constraints. This result is optimal assuming the Unique Games Conjecture.

The best previously known result, due ... more >>>

TR06-112 | 22nd August 2006
Xin Han, Kazuo Iwama, Deshi Ye, Guochuan Zhang

Strip Packing vs. Bin Packing

In this paper
we establish a general algorithmic framework between bin packing
and strip packing, with which we achieve the same asymptotic
bounds by applying bin packing algorithms to strip packing. More
precisely we obtain the following results: (1) Any offline bin
packing algorithm can be applied to strip packing ... more >>>

TR07-104 | 15th September 2007
Moses Charikar, Konstantin Makarychev, Yury Makarychev

On the Advantage over Random for Maximum Acyclic Subgraph

In this paper we present a new approximation algorithm for the MAX ACYCLIC SUBGRAPH problem. Given an instance where the maximum acyclic subgraph contains (1/2 + delta) fraction of all edges, our algorithm finds an acyclic subgraph with (1/2 + Omega(delta/ log n)) fraction of all edges.

more >>>

TR09-021 | 2nd March 2009
Konstantin Makarychev, Yury Makarychev

How to Play Unique Games on Expanders

In this note we improve a recent result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders.

Given a (1 - epsilon)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignments satisfying at least a (1 - C ... more >>>

TR11-019 | 5th February 2011
Valentin Brimkov, Andrew Leach, Jimmy Wu, Michael Mastroianni

On the Approximability of a Geometric Set Cover Problem

Given a finite set of straight line segments $S$ in $R^{2}$ and some $k\in N$, is there a subset $V$ of points on segments in $S$ with $\vert V \vert \leq k$ such that each segment of $S$ contains at least one point in $V$? This is a special case ... more >>>

TR14-066 | 17th April 2014
Suguru Tamaki, Yuichi Yoshida

Robust Approximation of Temporal CSP

A temporal constraint language $\Gamma$ is a set of relations with first-order definitions in $({\mathbb{Q}}; <)$. Let CSP($\Gamma$) denote the set of constraint satisfaction problem instances with relations from $\Gamma$. CSP($\Gamma$) admits robust approximation if, for any $\varepsilon \geq 0$, given a $(1-\varepsilon)$-satisfiable instance of CSP($\Gamma$), we can compute an ... more >>>

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