Anna Adamaszek

Almost tight bounds for reordering buffer management

We give almost tight bounds for the online reordering buffer management problem on the uniform metric. Specifically, we present the first non-trivial lower bounds for this problem by showing that deterministic online algorithms have a competitive ratio of at least Ω(√{log k/log log k}) and randomized online algorithms have a competitive ratio of at least Ω(log log k), where k denotes the size of the buffer. We complement this by presenting a deterministic online algorithm for the reordering buffer management problem that obtains a competitive ratio of O(√log k), almost matching the lower bound. This improves upon an algorithm by Avigdor-Elgrabli and Rabani (SODA 2010) that achieves a competitive ratio of O(log k/ log log k).

PTAS for k-Tour Cover Problem on the Plane for Moderately Large Values of k

Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P. The k-tour cover problem is known to be

Optimal online buffer scheduling for block devices

\mathcal{NP}

Large-Girth Roots of Graphs

-hard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomial-time approximation scheme (PTAS) for small values of k,

PTAS for k-tour cover poblem on the plane for moderately large values of k

k=\O(\log n / \log\log n)

Combinatorics of the change-making problem

. In this paper, we significantly enlarge the set of values of k for which a PTAS is provable. We present a new PTAS for all values of

Approximation and Hardness Results for the Maximum Edge q -coloring Problem

k \le 2^{\log^{\delta}n}

Submodular unsplittable flow on trees

, where ? = ?(?). The main technical result proved in the paper is a novel reduction of the k-tour cover problem with a set of n points to a small set of instances of the problem, each with

Reordering buffer management with advice

\O((k/\epsilon)^{\O(1)})

Hardness of Approximation for Strip Packing

points.