The Cycle Packing problem asks whether a given undirected graph G = (V,E) contains k vertex-disjoint cycles. Since the publication of the classic Erdős-Pósa theorem in 1965, this problem received significant scientific attention in the fields of Graph Theory and Algorithm Design. In particular, this problem is one of the first problems studied in the framework of Parameterized Complexity. The n...

We prove that, for any quantum evolution in`2 (Z D), there exist arbitrarily long time scales on which the qth moment of the position operator increases at least as fast as a power of time given by q=D times the packing dimension of the spectral measure. Packing dimensions of measures and their connections to scaling exponents and box-counting dimensions are also discussed.

In this paper we give a short survey on eecient algorithms for Steiner trees and paths packing problems in planar graphs. We particularly concentrate on recent results. The rst result is a linear-time algorithm for packing vertex-disjoint trees resp. paths within a planar graph, where the vertices to be connected lie on at most two diierent faces 26, 32]. This algorithm is based on a linear-tim...

original paper   the mass-transfer media plays a significant role on the performance of a packed tower. in this paper three counter-current single-stage packed towers at laboratory scale, randomly packed with two different sizes of two types of packing material were experimentally tested to study the role of the packing on the performance of them in the removal of sulfuric acid mists. gas sampl...

An instance of the two-dimensional strip packing problem is specified by n rectangular items, each having a width, 0 < wn ≤ 1, and height, 0 < hn ≤ 1. The objective is to place these items into a strip of width 1, without rotations, such that they are nonoverlapping and the total height of the resulting packing is minimized. In this thesis, we consider the version of the twodimensional strip pa...

We describe sequential and parallel algorithms that approximately solve linear programs with no negative coefficients (a.k.a. mixed packing and covering problems). For explicitly given problems, our fastest sequential algorithm returns a solution satisfying all constraints within a 1 ± ǫ factor in O(md log(m)/ǫ) time, where m is the number of constraints and d is the maximum number of constrain...

We investigate whether kernelization results can be obtained if we restrict kernelization algorithms to run in logarithmic space. This restriction for kernelization is motivated by the question of what results are attainable for preprocessing via simple and/or local reduction rules. We find kernelizations for d-hitting set(k), d-set packing(k), edge dominating set(k) and a number of hitting and...

In this paper, we extend the classical Variable Size Bin Packing Problem (VS-BPP) by adding time features to both bins and items. Specifically, the bins act as machines that process the assigned batch of items with a fixed processing time. Hence, the items are available for processing at given times and are penalized for tardiness. Within this extension we also consider a stochastic variant, wh...

We consider a game-theoretic bin packing problem and we study the convergence time to a Nash equilibrium. We show that, if the best-response strategy is used, then the number of steps needed to reach Nash equilibrium is O(mw2 max + nwmax) and O(nkwmax), where n, m, k and wmax denotes, resp., the number of items, the number of bins, the number of distinct item sizes, and the size of a largest item.