An L(h, 1, 1)-labeling of a graph is an assignment of labels from the set of integers {0, . . . , λ} to the nodes of the graph such
that adjacent nodes are assigned integers of at least distance h ≥ 1 apart and all nodes of distance three or less must be assigned different labels. The aim of the L(h, 1, 1)-labeling problem is to minimize λ, denoted by λh, 1, 1 and called span of the L(h, 1, 1)-labeling. As outerplanar graphs have bounded treewidth, the L(1, 1, 1)-labeling problem on outerplanar graphs can be exactly solved in O(n3), but the multiplicative factor depends on the maximum degree Δ and is too big to be of practical use. In this paper we give
a linear time approximation algorithm for computing the more general L(h, 1, 1)-labeling for outerplanar graphs that is within additive constants of the optimum values.
This research is partially supported by the European Research Project Algorithmic Principles for Building Efficient Overlay Computers (AEOLUS) and was done during the visit of Richard B. Tan at the Department of Computer Science, University of Rome “Sapienza”, supported
by a visiting fellowship from the University of Rome “Sapienza”. 相似文献
In this paper we study the one-way multiparty communication model, in which every party speaks exactly once in its turn. For every k, we prove a tight lower bound of Ω(n1/(k?1)}) on the probabilistic communication complexity of pointer jumping in a k-layered tree, where the pointers of the i-th layer reside on the forehead of the i-th party to speak. The lower bound remains nontrivial even for k = (logn)1/2?? parties, for any constant ? > 0. Previous to our work a lower bound was known only for k =3 (Wigderson, see [7]), and in restricted models for k>3 [2},24,18,4,13]. Our results have the following consequences to other models and problems, extending previous work in several directions. The one-way model is strong enough to capture general (not one-way) multiparty protocols with a bounded number of rounds. Thus we generalize two problem areas previously studied in the 2-party model (cf. [30,21,29]). The first is a rounds hierarchy: we give an exponential separation between the power of r and 2r rounds in general probabilistic k-party protocols, for any k and r. The second is the relative power of determinism and nondeterminism: we prove an exponential separation between nondeterministic and deterministic communication complexity for general k-party protocols with r rounds, for any k,r. The pointer jumping function is weak enough to be a special case of the well-studied disjointness function. Thus we obtain a lower bound of Ω(n1/(k?1)) on the probabilistic complexity of k-set disjointness in the one-way model, which was known only for k = 3 parties. Our result also extends a similar lower bound for the weaker simultaneous model, in which parties simultaneously send one message to a referee [12]. Finally, we infer an exponential separation between the power of any two different orders in which parties send messages in the one-way model, for every k. Previous results [29, 7] separated orders based on who speaks first. Our lower bound technique, which handles functions of high discrepancy over cylinder intersections, provides a “party-elimination” induction, based on a restricted form of a direct-product result, specific to the pointer jumping function. 相似文献
Here, we describe a simple approach to fabricate graphene-based field-effect-transistors (FETs), starting from aqueous solutions of graphene-oxide (GO), processed entirely under ambient conditions. The process relies on the site-selective reduction of GO sheets deposited in between or on the surface of micro/nanoelectrodes. The same electrodes are first used for voltage-induced electrochemical GO reduction, and then as the source and drain contacts of FETs, allowing for the straightforward production and characterization of ambipolar graphene devices. With the use of nanoelectrodes, we could reduce different selected areas belonging to one single sheet as well. 相似文献
By using a generic coarse grained polypeptide model, we perform multicanonical molecular dynamics simulations for determining the equilibrium conformation state diagram of a single homopolypeptide chain as a function of the chain length and temperature. The state diagram highlights the thermal regimes of stability for various conformational patterns in polypeptides, including swollen, random and collapsed coils, globular structures, extended and bended α helices, and compact β bundles. Remarkably, at low temperatures we observe a sharp transition from extended α helix to compact β bundles as the chain length increases. This finding indicates that the chain length is one of the intrisic factors that can trigger α-β transformations in a broad class of polypeptides. 相似文献
An overview of the vector and tensor Generalized Parton Distributions for a charged pion is presented. Such observables, belonging to the set of quantities fundamental for a detailed investigation of the hadronic inner dynamics, have been evaluated within a fully covariant Constituent Quark Model, based on a proper Ansatz of the pion Bethe–Salpeter Amplitude and the Mandelstam formula for matrix elements of operators acting on relativistic composite systems. Given the very encouraging results already obtained for the vector distribution of a charged pion, the model has been extended to the tensor one, and some preliminary calculations will be illustrated. 相似文献
We investigate the phase diagram of spinless bosons with long range (variant 1/r(3)) repulsive interactions, relevant to ultracold polarized atoms or molecules, using density matrix renormalization group. Between the two conventional insulating phases, the Mott and density wave phases, we find a new phase possessing hidden order revealed by nonlocal string correlations analogous to those characterizing the Haldane gapped phase of integer spin chains. We develop a mean field theory that describes the low-energy excitations in all three insulating phases. This is used to calculate the absorption spectrum due to oscillatory lattice modulation. We predict a sharp resonance in the spectrum due to a collective excitation of the new phase that would provide clear evidence for the existence of this phase. 相似文献
A simple, selective and highly sensitive method was developed and optimized to determine the most commonly used UV filters with endocrine-disrupting potential in water, namely benzophenone-3 (BP-3), octocrylene (OC), ethylhexyl dimethyl p-aminobenzoate (OD-PABA), ethylhexyl methoxycinnamate, ethylhexyl salicylate (EHS) and homosalate (HMS). Samples were extracted by stir bar sorptive extraction followed by liquid desorption (SBSE-LD). The important factors influencing SBSE-LD were optimized. Under optimal conditions, assays were performed on 50 mL of water sample using stir bars (0.5 mm in film thickness, 10 mm in length) at room temperature. The analytes were determined by liquid chromatography–tandem mass spectrometry with triple quadrupole analyzer using atmospheric pressure chemical ionization. The main parameters in HPLC–APCI–MS/MS were also optimized to provide the best performances for all analytes. Moreover, matrix effect was investigated using two methods the post-column infusion system and the method of spiked matrices after extraction. As a result, no significant matrix effect on the analysis was observed. The method showed good linearity (R2 coefficients greater than 0.996 in different water samples after SBSE-LD). Recoveries of the analytes were close to 90%, except for BP-3 (64%) and OC (76%) with relative standard deviation lower than 11%. Detection limits were between 0.6 and 3.3 ng L−1 for all the analytes except for HMS (94 ng L−1) and EHS (114 ng L−1). This methodology was applied to measure UV filters in seawater, river water and wastewater in different sites of Liguria; BP-3 and OC were found in most of the considered samples at rather low concentration level.
We introduce the notion of τ‐like partial order, where τ is one of the linear order types ω, ω*, ω + ω*, and ζ. For example, being ω‐like means that every element has finitely many predecessors, while being ζ‐like means that every interval is finite. We consider statements of the form “any τ‐like partial order has a τ‐like linear extension” and “any τ‐like partial order is embeddable into τ” (when τ is ζ this result appears to be new). Working in the framework of reverse mathematics, we show that these statements are equivalent either to $\mathsf {B}{\Sigma }^{0}_{2}$ or to $\mathsf {ACA}_0$ over the usual base system $\mathsf {RCA}_0$. 相似文献