Greedy Algorithms for Steiner Forest

In the Steiner Forest problem, we are given terminal pairs $\{s_i, t_i\}$, and need to find the cheapest subgraph which connects each of the terminal pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson gave primal-dual constant-factor approximation algorithms for this problem; until now, the only constant-factor approximations we know are via linear programming relaxations. We consider the following greedy algorithm: Given terminal pairs in a metric space, call a terminal "active" if its distance to its partner is non-zero. Pick the two closest active terminals (say $s_i, t_j$), set the distance between them to zero, and buy a path connecting them. Recompute the metric, and repeat. Our main result is that this algorithm is a constant-factor approximation. We also use this algorithm to give new, simpler constructions of cost-sharing schemes for Steiner forest. In particular, the first "group-strict" cost-shares for this problem implies a very simple combinatorial sampling-based algorithm for stochastic Steiner forest

The role of Ar III in quantitative spectroscopy on hot argon plasmas

We perform quantitative optical emission spectroscopy on the hot core of the cathode region of a free-burning arc in argon under atmospheric pressure. As the peak temperatures in the centre of the discharge exceed 22 000 K we are able to observe three spectra of argon (Ar I, Ar II and Ar III) and the continuum emission. We report on some inconsistencies concerning the evaluation of Ar III radiation in both line and continuum emission. These are caused by erroneous data in the literature and common misconceptions about the influence of Ar III on the plasma emission. We discuss the impact of this fact on published data

A 2k2k-Vertex Kernel for Maximum Internal Spanning Tree

We consider the parameterized version of the maximum internal spanning tree problem, which, given an $n$-vertex graph and a parameter $k$, asks for a spanning tree with at least $k$ internal vertices. Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a $3k$-vertex kernel. Here we propose a novel way to use the same reduction rule, resulting in an improved $2k$-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a deterministic algorithm for the problem running in time $4^k \cdot n^{O(1)}$

Zeeman energy and spin relaxation in a one-electron quantum dot

We have measured the relaxation time, T1, of the spin of a single electron confined in a semiconductor quantum dot (a proposed quantum bit). In a magnetic field, applied parallel to the two-dimensional electron gas in which the quantum dot is defined, Zeeman splitting of the orbital states is directly observed by measurements of electron transport through the dot. By applying short voltage pulses, we can populate the excited spin state with one electron and monitor relaxation of the spin. We find a lower bound on T1 of 50 microseconds at 7.5 T, only limited by our signal-to-noise ratio. A continuous measurement of the charge on the dot has no observable effect on the spin relaxation.Comment: Replaced with the version published in Phys. Rev. Let

Impurity effects in quantum dots: Toward quantitative modeling

We have studied the single-electron transport spectrum of a quantum dot in GaAs/AlGaAs resonant tunneling device. The measured spectrum has irregularities indicating a broken circular symmetry. We model the system with an external potential consisting of a parabolic confinement and a negatively charged Coulombic impurity placed in the vicinity of the quantum dot. The model leads to good agreement between the calculated single-electron eigenenergies and the experimental spectrum. Furthermore, we use the spin-density-functional theory to study the energies and angular momenta when the system contains many interacting electrons. In the high magnetic field regime the increasing electron number is shown to reduce the distortion induced by the impurity.Peer reviewe

Approximating the minimum directed tree cover

Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a rooted directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover problem (DTCP) is to find a directed tree cover of minimum cost. The problem is known to be $NP$-hard. In this paper, we show that the weighted Set Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to approximate DTCP with the same ratio as for SCP. We show that this expectation can be satisfied in some way by designing a purely combinatorial approximation algorithm for the DTCP and proving that the approximation ratio of the algorithm is $\max\{2, \ln(D^+)\}$ with $D^+$ is the maximum outgoing degree of the nodes in $G$.Comment: 13 page

Ground-state characterization of Nb charge-phase Josephson qubits

We present investigations of Josephson charge-phase qubits inductively coupled to a radio-frequency driven tank-circuit enabling the readout of the states by measuring the Josephson inductance of the qubit. The circuits including junctions with linear dimensions of 60 nm and 80 nm are fabricated from Nb trilayer and allowing the determination of relevant sample parameters at liquid helium temperature. The observed partial suppression of the circulating supercurrent at 4.2 K is explained in the framework of a quantum statistical model. We have probed the ground-state properties of qubit structures with different ratios of the Josephson coupling to Coulomb charging energy at 20 mK, demonstrating both the magnetic control of phase and the electrostatic control of charge on the qubit island.Comment: 8 pages, 8 figure

Approximate Deadline-Scheduling with Precedence Constraints

We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result is an O(log k)-approximation algorithm for instances with k distinct job deadlines

Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

TRAVEL WATTLE OF LANDSCAPES, ANTIQUITY AND SPIRITUAL AURA OF SPACE IN TRAVELOGUES BY ZLATKO TOMIČIĆ

U radu se prvi put revalorizira još posve neistražen književni opus tiskanih putopisnih zbirka istaknutoga suvremenog hrvatskog književnika Zlatka Tomičića (Zagreb, 1930. – Zagreb, 2008.). Današnja međunarodna književna produkcija snažno je usmjerena prema oblikovanjima tzv. nefikcionalnih žanrova (memoara, putopisa, autobiografija) pa se prema ulozi reanimiranja misaonoga poklisara realiziraju i Tomičićevi putopisi. Tomičićeva putopisna proza jednim se dijelom promatra u kontekstu njegovih književnih suvremenika i političko-društvene sudbine autora. Međutim rad se u prvome planu usmjerava na književnu analizu i interpretaciju šesnaest putopisnih knjiga te se unutar autorova oblikotvornoga postupka promatraju i njegovi književni utjecaji, književne relacije i refleksivno-filozofski obzori. Bitna konstanta Tomičićeva putopisa jest težnja za polifonijskim i polihistorijskim modelom doživljavanja svijeta. Kao obilježje Tomičićeva umjetničkoga postupka izdvaja se interferencijska realizacija hibridnoga žanra putopisa i stvaranje književnoga pletera, tj. ispreplitanja kozmopolitizma i rodoljublja te povezivanja realističkih zapažanja s konstantom kulturno-duhovne aure opisivanoga prostora.The paper valorizes for the first time a completely unexplored literary opus of published travelogue collections of prominent contemporary Croatian writer Zlatko Tomičić (Zagreb, 1930. – Zagreb, 2008.). Contemporary international literary production is strongly directed to forming of the so called non-fictional genres (memoirs, travelogues, autobiographies), therefore Tomičić’s travelogues are also realized in accordance with the role of reanimating contemplative envoy. Tomičić’s travel prose is partly considered in the context of his literary contemporaries and authors’ political-social destiny. However, the paper is in the first plan directed to literary analysis and interpretation of sixteen travelogues and author’s literary influences, literary relations and reflexive-philosophic visions are considered within his forming procedure. A very important constant of author’s travelogue is aspiration to polyphonic and historic model of life experiencing. The characteristic of Tomičić’s artistic procedure is interferential realization of hybrid travelogue genre and creation of literary wattle i.e. interweaving of cosmopolitism and patriotism and connecting of realistic observations with a constant of cultural-spiritual aura of described space