Scheduling Packets with Values and Deadlines in Size-bounded Buffers

Motivated by providing quality-of-service differentiated services in the Internet, we consider buffer management algorithms for network switches. We study a multi-buffer model. A network switch consists of multiple size-bounded buffers such that at any time, the number of packets residing in each individual buffer cannot exceed its capacity. Packets arrive at the network switch over time; they have values, deadlines, and designated buffers. In each time step, at most one pending packet is allowed to be sent and this packet can be from any buffer. The objective is to maximize the total value of the packets sent by their respective deadlines. A 9.82-competitive online algorithm has been provided for this model (Azar and Levy. SWAT 2006), but no offline algorithms have been known yet. In this paper, We study the offline setting of the multi-buffer model. Our contributions include a few optimal offline algorithms for some variants of the model. Each variant has its unique and interesting algorithmic feature. These offline algorithms help us understand the model better in designing online algorithms.Comment: 7 page

Random graph model with power-law distributed triangle subgraphs

Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance of small subgraphs is important. Here, we study the arrangement of triangles in a model for scale-free random graphs and determine the asymptotic behavior of the clustering coefficient, the average number of triangles, as well as the number of triangles attached to the vertex of maximum degree. We prove that triangles are power-law distributed among vertices and characterized by both vertex and edge coagulation when the degree exponent satisfies $2<\beta<2.5$; furthermore, a finite density of triangles appears as $\beta=2+1/3$.Comment: 4 pages, 2 figure; v2: major conceptual change

Searching in Unstructured Overlays Using Local Knowledge and Gossip

This paper analyzes a class of dissemination algorithms for the discovery of distributed contents in Peer-to-Peer unstructured overlay networks. The algorithms are a mix of protocols employing local knowledge of peers' neighborhood and gossip. By tuning the gossip probability and the depth k of the k-neighborhood of which nodes have information, we obtain different dissemination protocols employed in literature over unstructured P2P overlays. The provided analysis and simulation results confirm that, when properly configured, these schemes represent a viable approach to build effective P2P resource discovery in large-scale, dynamic distributed systems.Comment: A revised version of the paper appears in Proc. of the 5th International Workshop on Complex Networks (CompleNet 2014) - Studies in Computational Intelligence Series, Springer-Verlag, Bologna (Italy), March 201

A Protocol for Generating Random Elements with their Probabilities

We give an AM protocol that allows the verifier to sample elements x from a probability distribution P, which is held by the prover. If the prover is honest, the verifier outputs (x, P(x)) with probability close to P(x). In case the prover is dishonest, one may hope for the following guarantee: if the verifier outputs (x, p), then the probability that the verifier outputs x is close to p. Simple examples show that this cannot be achieved. Instead, we show that the following weaker condition holds (in a well defined sense) on average: If (x, p) is output, then p is an upper bound on the probability that x is output. Our protocol yields a new transformation to turn interactive proofs where the verifier uses private random coins into proofs with public coins. The verifier has better running time compared to the well-known Goldwasser-Sipser transformation (STOC, 1986). For constant-round protocols, we only lose an arbitrarily small constant in soundness and completeness, while our public-coin verifier calls the private-coin verifier only once

Observation of Goos-H\"{a}nchen shifts in metallic reflection

We report the first observation of the Goos-H$\rm \ddot{\textbf{a}}$nchen shift of a light beam incident on a metal surface. This phenomenon is particularly interesting because the Goos-H$\rm \ddot{\textbf{a}}$nchen shift for $p$ polarized light in metals is negative and much bigger than the positive shift for $s$ polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface when this is excited by a $p$ polarized beam of light.Comment: The parer was published on Optics Express. The new version is modified according to the reviewers suggestion

Observation of OAM sidebands due to optical reflection

We investigate how the orbital angular momentum (OAM) of a paraxial light beam is affected upon reflection at a planar interface. Theoretically, the unavoidable angular spread of the (paraxial) beam leads to OAM sidebands which are found to be already significant for modest beam spread (0.05). In analogy to the polarization Fresnel coefficients we develop a theory based upon spatial Fresnel coefficients; this allows straightforward prediction of the strength of the sidebands. We confirm this by experiment.Comment: 5 page

Interstellar Carbon in Translucent Sightlines

We report interstellar C II column densities or upper limits determined from weak absorption of the 2325.4029 A intersystem transition observed in six translucent sightlines with STIS. The sightlines sample a wide range of interstellar characteristics including total-to-selective extinction, R_{V} = 2.6 - 5.1; average hydrogen density along the sightline, = 3 - 14 cm^{-3}; and fraction of H in molecular form, 0 - 40%. Four of the sightlines, those toward HD 37021, HD 37061, HD 147888 and HD 207198, have interstellar gas-phase abundances that are consistent with the diffuse sightline ratio of 161 +/- 17 carbon atoms in the gas per million hydrogen nuclei. We note that while it has a gas-phase carbon abundance that is consistent with the other sightlines, a large fraction of the C II toward HD 37061 is in an excited state. The sightline toward HD 152590 has a measured interstellar gas-phase carbon abundance that is well above the diffuse sightline average; the column density of C in this sightline may be overestimated due to noise structure in the data. Toward HD 27778 we find a 3 sigma abundance upper limit of <108 C atoms in the gas per million H, a substantially enhanced depletion of C as compared to the diffuse sightline value. The interstellar characteristics toward HD 27778 are otherwise not extreme among the sample except for an unusually large abundance of CO molecules in the gas.Comment: Accepted for publication in the Astrophysical Journa