Serving Online Requests with Mobile Servers

We study an online problem in which a set of mobile servers have to be moved in order to efficiently serve a set of requests that arrive in an online fashion. More formally, there is a set of $n$ nodes and a set of $k$ mobile servers that are placed at some of the nodes. Each node can potentially host several servers and the servers can be moved between the nodes. There are requests $1,2,\ldots$ that are adversarially issued at nodes one at a time. An issued request at time $t$ needs to be served at all times $t' \geq t$. The cost for serving the requests is a function of the number of servers and requests at the different nodes. The requirements on how to serve the requests are governed by two parameters $\alpha\geq 1$ and $\beta\geq 0$. An algorithm needs to guarantee at all times that the total service cost remains within a multiplicative factor of $\alpha$ and an additive term $\beta$ of the current optimal service cost. We consider online algorithms for two different minimization objectives. We first consider the natural problem of minimizing the total number of server movements. We show that in this case for every $k$, the competitive ratio of every deterministic online algorithm needs to be at least $\Omega(n)$. Given this negative result, we then extend the minimization objective to also include the current service cost. We give almost tight bounds on the competitive ratio of the online problem where one needs to minimize the sum of the total number of movements and the current service cost. In particular, we show that at the cost of an additional additive term which is roughly linear in $k$, it is possible to achieve a multiplicative competitive ratio of $1+\varepsilon$ for every constant $\varepsilon>0$.Comment: 25 page

The Cost of Global Broadcast in Dynamic Radio Networks

We study the single-message broadcast problem in dynamic radio networks. We show that the time complexity of the problem depends on the amount of stability and connectivity of the dynamic network topology and on the adaptiveness of the adversary providing the dynamic topology. More formally, we model communication using the standard graph-based radio network model. To model the dynamic network, we use a generalization of the synchronous dynamic graph model introduced in [Kuhn et al., STOC 2010]. For integer parameters $T\geq 1$ and $k\geq 1$, we call a dynamic graph $T$-interval $k$-connected if for every interval of $T$ consecutive rounds, there exists a $k$-vertex-connected stable subgraph. Further, for an integer parameter $\tau\geq 0$, we say that the adversary providing the dynamic network is $\tau$-oblivious if for constructing the graph of some round $t$, the adversary has access to all the randomness (and states) of the algorithm up to round $t-\tau$. As our main result, we show that for any $T\geq 1$, any $k\geq 1$, and any $\tau\geq 1$, for a $\tau$-oblivious adversary, there is a distributed algorithm to broadcast a single message in time $O\big(\big(1+\frac{n}{k\cdot\min\left\{\tau,T\right\}}\big)\cdot n\log^3 n\big)$. We further show that even for large interval $k$-connectivity, efficient broadcast is not possible for the usual adaptive adversaries. For a $1$-oblivious adversary, we show that even for any $T\leq (n/k)^{1-\varepsilon}$ (for any constant $\varepsilon>0$) and for any $k\geq 1$, global broadcast in $T$-interval $k$-connected networks requires at least $\Omega(n^2/(k^2\log n))$ time. Further, for a $0$ oblivious adversary, broadcast cannot be solved in $T$-interval $k$-connected networks as long as $T<n-k$.Comment: 17 pages, conference version appeared in OPODIS 201

Dynamic Analysis of the Arrow Distributed Directory Protocol in General Networks

The Arrow protocol is a simple and elegant protocol to coordinate exclusive access to a shared object in a network. The protocol solves the underlying distributed queueing problem by using path reversal on a pre-computed spanning tree (or any other tree topology simulated on top of the given network). It is known that the Arrow protocol solves the problem with a competitive ratio of O(log D) on trees of diameter D. This implies a distributed queueing algorithm with competitive ratio O(s log D) for general networks with a spanning tree of diameter D and stretch s. In this work we show that when running the Arrow protocol on top of the well-known probabilistic tree embedding of Fakcharoenphol, Rao, and Talwar [STOC\u2703], we obtain a randomized distributed online queueing algorithm with expected competitive ratio O(log n) against an oblivious adversary even on general n-node network topologies. The result holds even if the queueing requests occur in an arbitrarily dynamic and concurrent fashion and even if communication is asynchronous. The main technical result of the paper shows that the competitive ratio of the Arrow protocol is constant on a special family of tree topologies, known as hierarchically well separated trees

Concurrent Distributed Serving with Mobile Servers

This paper introduces a new resource allocation problem in distributed computing called distributed serving with mobile servers (DSMS). In DSMS, there are k identical mobile servers residing at the processors of a network. At arbitrary points of time, any subset of processors can invoke one or more requests. To serve a request, one of the servers must move to the processor that invoked the request. Resource allocation is performed in a distributed manner since only the processor that invoked the request initially knows about it. All processors cooperate by passing messages to achieve correct resource allocation. They do this with the goal to minimize the communication cost. Routing servers in large-scale distributed systems requires a scalable location service. We introduce the distributed protocol Gnn that solves the DSMS problem on overlay trees. We prove that Gnn is starvation-free and correctly integrates locating the servers and synchronizing the concurrent access to servers despite asynchrony, even when the requests are invoked over time. Further, we analyze Gnn for "one-shot" executions, i.e., all requests are invoked simultaneously. We prove that when running Gnn on top of a special family of tree topologies - known as hierarchically well-separated trees (HSTs) - we obtain a randomized distributed protocol with an expected competitive ratio of O(log n) on general network topologies with n processors. From a technical point of view, our main result is that Gnn optimally solves the DSMS problem on HSTs for one-shot executions, even if communication is asynchronous. Further, we present a lower bound of Omega(max {k, log n/log log n}) on the competitive ratio for DSMS. The lower bound even holds when communication is synchronous and requests are invoked sequentially

Substitutional doping of Cu in diamond: Mott physics with pp orbitals

Discovery of superconductivity in the impurity band formed by heavy doping of boron into diamond (C:B) as well as doping of boron into silicon (Si:B) has provided a rout for the possibility of new families of superconducting materials. Motivated by the special role played by copper atoms in high temperature superconducting materials where essentially Cu $d$ orbitals are responsible for a variety of correlation induced phases, in this paper we investigate the effect of substitutional doping of Cu into diamond. Our extensive first principle calculations averaged over various geometries based on density functional theory, indicates the formation of a mid-gap band, which mainly arises from the $t_{2g}$ and $4p$ states of Cu. For impurity concentrations of more than $\sim 1$2p$bands of neighboring carbon atoms can be ignored. Based on our detailed analysis, we suggest a two band model for the mid-gap states consisting of a quarter-filled hole like$t_{2g}$band, and a half-filled band of$4p$states. Increasing the concentration of the Cu impurity beyond$\sim 5%, completely closes the spectral gap of the host diamond.Comment: 5 figure

Investigation of bias current and modulation frequency dependences of detectivity of YBCO TES and the effects of coating of Cu-C composite absorber layer

Bolometric response and noise characteristics of YBCO superconductor transition edge IR detectors with relatively sharp transition and its resulting detectivity are investigated both theoretically and experimentally. The magnitude of response of a fabricated device was obtained for different bias currents and modulation frequencies. Using the measured and calculated bolometric response and noise characteristics, we found and analyzed the device detectivity versus frequency for different bias currents. The detectivity versus chopping frequency of the device did not decrease following the response strongly, due to the decrease of the noise at higher frequencies up to 1 kHz, resulting in maximum detectivity around the modulation frequency of 100 Hz. We also improved the responsivity of the device through the increase of the surface absorption by using a novel infrared absorber, which is made of a copper-carbon composite, coated in a low-temperature process. Within the modulation frequency range studied in this paper, comparison of device detectivity before and after coating is also presented. © 2009 IEEE

Cu-ZrO2 catalysts with highly dispersed Cu nanoclusters derived from ZrO2@ HKUST-1 composites for the enhanced CO2 hydrogenation to methanol

In this study, a series of Cu-ZrO2 catalysts with highly dispersed Cu nanoclusters were prepared via the calcination and reduction of ZrO2@HKUST-1 precursors. These catalysts demonstrated an outstanding selectivity in the yield of methanol during CO2 hydrogenation. The space-time yield (STY) of methanol is 5.2 times higher than that of those similar catalysts reported by other researchers, which were prepared using conventional method and tested under the same testing conditions. Density functional theory (DFT) study revealed that the activation of CO2 occurs at the Cu-ZrO2 interfaces and facilitates the hydrogenation of CO2 to methanol. It is concluded that the controlled formation of the highly dispersed Cu nanoclusters not only provides a large number of highly efficient active centers for CO2 hydrogenation, but also leads the generation of more Cu-ZrO2 interfaces. These two effects contribute to the superior catalytic performance of the nano Cu-ZrO2 catalyst in CO2 hydrogenation