Min-Max Theorems for Packing and Covering Odd (u,v)(u,v)-trails

We investigate the problem of packing and covering odd $(u,v)$-trails in a graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated vertices but no repeated edges. We call a trail odd if the number of edges in the trail is odd. Let $\nu(u,v)$ denote the maximum number of edge-disjoint odd $(u,v)$-trails, and $\tau(u,v)$ denote the minimum size of an edge-set that intersects every odd $(u,v)$-trail. We prove that $\tau(u,v)\leq 2\nu(u,v)+1$. Our result is tight---there are examples showing that $\tau(u,v)=2\nu(u,v)+1$---and substantially improves upon the bound of $8$ obtained in [Churchley et al 2016] for $\tau(u,v)/\nu(u,v)$. Our proof also yields a polynomial-time algorithm for finding a cover and a collection of trails satisfying the above bounds. Our proof is simple and has two main ingredients. We show that (loosely speaking) the problem can be reduced to the problem of packing and covering odd $(uv,uv)$-trails losing a factor of 2 (either in the number of trails found, or the size of the cover). Complementing this, we show that the odd-$(uv,uv)$-trail packing and covering problems can be tackled by exploiting a powerful min-max result of [Chudnovsky et al 2006] for packing vertex-disjoint nonzero $A$-paths in group-labeled graphs

High performance communication subsystem for clustering standard high-volume servers using Gigabit Ethernet

This paper presents an efficient communication subsystem, DP-II, for clustering standard high-volume (SHV) servers using Gigabit Ethernet. The DP-II employs several lightweight messaging mechanisms to achieve low-latency and high-bandwidth communication. The test shows an 18.32 us single-trip latency and 72.8 MB/s bandwidth on a Gigabit Ethernet network for connecting two Dell PowerEdge 6300 Quad Xeon SMP servers running Linux. To improve the programmability of the DP-II communication subsystem, the development of DP-II was based on a concise yet powerful abstract communication model, Directed Point Model, which can be conveniently used to depict the inter-process communication pattern of a parallel task in the cluster environment. In addition, the API of DP-II preserves the syntax and semantics of traditional UNIX I/O operations, which make it easy to use.published_or_final_versio

Simultaneous temperature and refractive index measurements using a 3°slanted multimode fiber Bragg grating

Author name used in this publication: M. S. DemokanAuthor name used in this publication: W. Jin2005-2006 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Mimimal Length Uncertainty Principle and the Transplanckian Problem of Black Hole Physics

The minimal length uncertainty principle of Kempf, Mangano and Mann (KMM), as derived from a mutilated quantum commutator between coordinate and momentum, is applied to describe the modes and wave packets of Hawking particles evaporated from a black hole. The transplanckian problem is successfully confronted in that the Hawking particle no longer hugs the horizon at arbitrarily close distances. Rather the mode of Schwarzschild frequency $\omega$ deviates from the conventional trajectory when the coordinate $r$ is given by $| r - 2M|\simeq \beta_H \omega / 2 \pi$ in units of the non local distance legislated into the uncertainty relation. Wave packets straddle the horizon and spread out to fill the whole non local region. The charge carried by the packet (in the sense of the amount of "stuff" carried by the Klein--Gordon field) is not conserved in the non--local region and rapidly decreases to zero as time decreases. Read in the forward temporal direction, the non--local region thus is the seat of production of the Hawking particle and its partner. The KMM model was inspired by string theory for which the mutilated commutator has been proposed to describe an effective theory of high momentum scattering of zero mass modes. It is here interpreted in terms of dissipation which gives rise to the Hawking particle into a reservoir of other modes (of as yet unknown origin). On this basis it is conjectured that the Bekenstein--Hawking entropy finds its origin in the fluctuations of fields extending over the non local region.Comment: 12 pages (LateX), 1 figur

Chinese herbal medicine in the treatment of acute upper respiratory tract infection: a randomised, double blind, placebo-controlled clinical trial.

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Inbuilt Mechanisms for Overcoming Functional Problems Inherent in Hepatic Microlobular Structure

This paper is funded by an MRC/EPSRC Discipline Bridging Initiative Grant (G0502256-77947) to W. Wan

Explosion Mechanisms of Core-Collapse Supernovae

Supernova theory, numerical and analytic, has made remarkable progress in the past decade. This progress was made possible by more sophisticated simulation tools, especially for neutrino transport, improved microphysics, and deeper insights into the role of hydrodynamic instabilities. Violent, large-scale nonradial mass motions are generic in supernova cores. The neutrino-heating mechanism, aided by nonradial flows, drives explosions, albeit low-energy ones, of ONeMg-core and some Fe-core progenitors. The characteristics of the neutrino emission from new-born neutron stars were revised, new features of the gravitational-wave signals were discovered, our notion of supernova nucleosynthesis was shattered, and our understanding of pulsar kicks and explosion asymmetries was significantly improved. But simulations also suggest that neutrino-powered explosions might not explain the most energetic supernovae and hypernovae, which seem to demand magnetorotational driving. Now that modeling is being advanced from two to three dimensions, more realism, new perspectives, and hopefully answers to long-standing questions are coming into reach.Comment: 35 pages, 11 figures (29 eps files; high-quality versions can be obtained upon request); accepted by Annual Review of Nuclear and Particle Scienc

Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror

Author name used in this publication: M. S. Demokan2004-2005 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Run Generation Revisited: What Goes Up May or May Not Come Down

In this paper, we revisit the classic problem of run generation. Run generation is the first phase of external-memory sorting, where the objective is to scan through the data, reorder elements using a small buffer of size M , and output runs (contiguously sorted chunks of elements) that are as long as possible. We develop algorithms for minimizing the total number of runs (or equivalently, maximizing the average run length) when the runs are allowed to be sorted or reverse sorted. We study the problem in the online setting, both with and without resource augmentation, and in the offline setting. (1) We analyze alternating-up-down replacement selection (runs alternate between sorted and reverse sorted), which was studied by Knuth as far back as 1963. We show that this simple policy is asymptotically optimal. Specifically, we show that alternating-up-down replacement selection is 2-competitive and no deterministic online algorithm can perform better. (2) We give online algorithms having smaller competitive ratios with resource augmentation. Specifically, we exhibit a deterministic algorithm that, when given a buffer of size 4M , is able to match or beat any optimal algorithm having a buffer of size M . Furthermore, we present a randomized online algorithm which is 7/4-competitive when given a buffer twice that of the optimal. (3) We demonstrate that performance can also be improved with a small amount of foresight. We give an algorithm, which is 3/2-competitive, with foreknowledge of the next 3M elements of the input stream. For the extreme case where all future elements are known, we design a PTAS for computing the optimal strategy a run generation algorithm must follow. (4) Finally, we present algorithms tailored for nearly sorted inputs which are guaranteed to have optimal solutions with sufficiently long runs

Adaptive live VM migration over a WAN: modeling and implementation

Recent advances in virtualization technology enable high mobility of virtual machines and resource provisioning at the data-center level. To streamline the migration process, various migration strategies have been proposed for VM live migration over a local-area network (LAN). The most common solution uses memory pre-copying and assumes the storage is shared on the LAN. While applied to a wide-area network (WAN), the VM live migration algorithms need a new design philosophy to address the challenges of long latency, limited bandwidth, unstable network conditions and the movement of storage. This paper proposes a three-phase fractional hybrid pre-copy and post-copy solution for both memory and storage to achieve highly adaptive migration over a WAN. In this hybrid solution, we selectively migrate an important fraction of memory and storage in the pre-copy and freeze-and-copy phase, while the rest (non-critical data set) is migrated during post-copying. We propose a new metric called performance restoration agility, which considers both the downtime and the VM speed degradation during the post-copy phase, to evaluate the migration process. We also develop a profiling framework and a novel probabilistic prediction model to adaptively find a predictably optimal combination of the memory and storage fractions to migrate. This model-based hybrid solution is implemented on Xen and evaluated in an emulated WAN environment. Experimental results show that our solution wins over all others in adaptiveness for various applications over a WAN, while retaining the responsiveness of post-copy algorithms.published_or_final_versio