Distributed Approximation Algorithms for Weighted Shortest Paths

A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth restriction} on edges (the standard synchronous \congest model). The question whether approximation algorithms help speed up the shortest paths (more precisely distance computation) was raised since at least 2004 by Elkin (SIGACT News 2004). The unweighted case of this problem is well-understood while its weighted counterpart is fundamental problem in the area of distributed approximation algorithms and remains widely open. We present new algorithms for computing both single-source shortest paths (\sssp) and all-pairs shortest paths (\apsp) in the weighted case. Our main result is an algorithm for \sssp. Previous results are the classic $O(n)$-time Bellman-Ford algorithm and an $\tilde O(n^{1/2+1/2k}+D)$-time $(8k\lceil \log (k+1) \rceil -1)$-approximation algorithm, for any integer $k\geq 1$, which follows from the result of Lenzen and Patt-Shamir (STOC 2013). (Note that Lenzen and Patt-Shamir in fact solve a harder problem, and we use $\tilde O(\cdot)$ to hide the O(\poly\log n) term.) We present an $\tilde O(n^{1/2}D^{1/4}+D)$-time $(1+o(1))$-approximation algorithm for \sssp. This algorithm is {\em sublinear-time} as long as $D$ is sublinear, thus yielding a sublinear-time algorithm with almost optimal solution. When $D$ is small, our running time matches the lower bound of $\tilde \Omega(n^{1/2}+D)$ by Das Sarma et al. (SICOMP 2012), which holds even when $D=\Theta(\log n)$, up to a \poly\log n factor.Comment: Full version of STOC 201

Fast Consensus under Eventually Stabilizing Message Adversaries

This paper is devoted to deterministic consensus in synchronous dynamic networks with unidirectional links, which are under the control of an omniscient message adversary. Motivated by unpredictable node/system initialization times and long-lasting periods of massive transient faults, we consider message adversaries that guarantee periods of less erratic message loss only eventually: We present a tight bound of $2D+1$ for the termination time of consensus under a message adversary that eventually guarantees a single vertex-stable root component with dynamic network diameter $D$, as well as a simple algorithm that matches this bound. It effectively halves the termination time $4D+1$ achieved by an existing consensus algorithm, which also works under our message adversary. We also introduce a generalized, considerably stronger variant of our message adversary, and show that our new algorithm, unlike the existing one, still works correctly under it.Comment: 13 pages, 5 figures, updated reference

Lubricated friction between incommensurate substrates

This paper is part of a study of the frictional dynamics of a confined solid lubricant film - modelled as a one-dimensional chain of interacting particles confined between two ideally incommensurate substrates, one of which is driven relative to the other through an attached spring moving at constant velocity. This model system is characterized by three inherent length scales; depending on the precise choice of incommensurability among them it displays a strikingly different tribological behavior. Contrary to two length-scale systems such as the standard Frenkel-Kontorova (FK) model, for large chain stiffness one finds that here the most favorable (lowest friction) sliding regime is achieved by chain-substrate incommensurabilities belonging to the class of non-quadratic irrational numbers (e.g., the spiral mean). The well-known golden mean (quadratic) incommensurability which slides best in the standard FK model shows instead higher kinetic-friction values. The underlying reason lies in the pinning properties of the lattice of solitons formed by the chain with the substrate having the closest periodicity, with the other slider.Comment: 14 pagine latex - elsart, including 4 figures, submitted to Tribology Internationa

Static friction on the fly: velocity depinning transitions of lubricants in motion

The dragging velocity of a model solid lubricant confined between sliding periodic substrates exhibits a phase transition between two regimes, respectively with quantized and with continuous lubricant center-of-mass velocity. The transition, occurring for increasing external driving force F_ext acting on the lubricant, displays a large hysteresis, and has the features of depinning transitions in static friction, only taking place on the fly. Although different in nature, this phenomenon appears isomorphic to a static Aubry depinning transition in a Frenkel-Kontorova model, the role of particles now taken by the moving kinks of the lubricant-substrate interface. We suggest a possible realization in 2D optical lattice experiments.Comment: 5 pages, 4 figures, revtex, in print in Phys. Rev. Let

Absolute Efficiency Measurements of NE-213 ORGANIC Phosphors for Detecting 14.4 and 2.6 Mev Neutrons

Efficiency measurements of organic phosphor scintillator for detecting 14.4 and 2.6 MeV neutron

Retroperitoneal fibrosis: a case of a patient (63y/o) treated with low-dose methotrexate (MTX) and 6-methylprednisolone (6-MP)

Retroperitoneal fibrosis (RPF), is a rare fibroinflammatory disease. The pathogenesis of RPF is still unclear and numerous theories have been reported such as environmental factors, immunologic process, genetic component, local inflammation and advanced atherosclerosis. RPF is characterized by the presence of a particular retroperitoneal fibrotic tissue which is white, woody and involving retroperitoneal structures such as the great vessels, ureters and psoas muscle. The main complication of RPF is the obstruction of local structures such as the ureters due to the fibrosis and the treatment of this aspect represents the main challenge for this pathology. RPF medical treatment consists of corticosteroids or/and immunosuppressive therapy. We report a case of a patient (63y/o) affected by idiopathic RPF treated with low-dose methotrexate (MTX) and 6-methylprednisolone (6-MP) for two years, describing and confirming the effectiveness and safety of a long-term low-dose MTX and 6-MP treatment

Optimization by Quantum Annealing: Lessons from Simple Cases

This paper investigates the basic behavior and performance of simulated quantum annealing (QA) in comparison with classical annealing (CA). Three simple one dimensional case study systems are considered, namely a parabolic well, a double well, and a curved washboard. The time dependent Schr\"odinger evolution in either real or imaginary time describing QA is contrasted with the Fokker Planck evolution of CA. The asymptotic decrease of excess energy with annealing time is studied in each case, and the reasons for differences are examined and discussed. The Huse-Fisher classical power law of double well CA is replaced with a different power law in QA. The multi-well washboard problem studied in CA by Shinomoto and Kabashima and leading classically to a logarithmic annealing even in the absence of disorder, turns to a power law behavior when annealed with QA. The crucial role of disorder and localization is briefly discussed.Comment: 16 pages, 9 figure