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).

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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 >>>

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 >>>

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
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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 >>>

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 >>>

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 >>>

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 >>>

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 >>>

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.

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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 >>>

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 >>>

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 >>>