Distributed Exact Shortest Paths in Sublinear Time

The distributed single-source shortest paths problem is one of the most fundamental and central problems in the message-passing distributed computing. Classical Bellman-Ford algorithm solves it in $O(n)$ time, where $n$ is the number of vertices in the input graph $G$. Peleg and Rubinovich (FOCS'99) showed a lower bound of $\tilde{\Omega}(D + \sqrt{n})$ for this problem, where $D$ is the hop-diameter of $G$. Whether or not this problem can be solved in $o(n)$ time when $D$ is relatively small is a major notorious open question. Despite intensive research \cite{LP13,N14,HKN15,EN16,BKKL16} that yielded near-optimal algorithms for the approximate variant of this problem, no progress was reported for the original problem. In this paper we answer this question in the affirmative. We devise an algorithm that requires $O((n \log n)^{5/6})$ time, for $D = O(\sqrt{n \log n})$, and $O(D^{1/3} \cdot (n \log n)^{2/3})$ time, for larger $D$. This running time is sublinear in $n$ in almost the entire range of parameters, specifically, for $D = o(n/\log^2 n)$. For the all-pairs shortest paths problem, our algorithm requires $O(n^{5/3} \log^{2/3} n)$ time, regardless of the value of $D$. We also devise the first algorithm with non-trivial complexity guarantees for computing exact shortest paths in the multipass semi-streaming model of computation. From the technical viewpoint, our algorithm computes a hopset $G"$ of a skeleton graph $G'$ of $G$ without first computing $G'$ itself. We then conduct a Bellman-Ford exploration in $G' \cup G"$, while computing the required edges of $G'$ on the fly. As a result, our algorithm computes exactly those edges of $G'$ that it really needs, rather than computing approximately the entire $G'$

Radiation-induced insulator discharge pulses in the CRRES internal discharge monitor satellite experiment

The Internal Discharge Monitor (IDM) was designed to observe electrical pulses from common electrical insulators in space service. The sixteen insulator samples included twelve planar printed circuit boards and four cables. The samples were fully enclosed, mutually isolated, and space radiation penetrated 0.02 cm of aluminum before striking the samples. Pulsing began on the seventh orbit, the maximum pulse rate occurred on the seventeenth orbit when 13 pulses occurred, and the pulses slowly diminished to about one per 3 orbits six months later. After 8 months, the radiation belts abruptly increased and the pulse rates attained a new high. These pulse rates were in agreement with laboratory experience on shorter time scales. Several of the samples never pulsed. If the pulses were not confined within IDM, the physical processes could spread to become a full spacecraft anomaly. The IDM results indicate the rate at which small insulator pulses occur. Small pulses are the seeds of larger satellite electrical anomalies. The pulse rates are compared with space radiation intensities, L shell location, and spectral distributions from the radiation spectrometers on the Combined Release and Radiation Effects Satellite

Bulletin No. 288 - Draingage and Irrigation, Soil, Economic, and Social Conditions, Delta Area, Utah Division 4: Social Conditions

This study is a part of a more comprehensive one which was organized in 1928 for the purpose of ascertaining what conditions existed in bonded irrigation and drainage districts which were unable to. liquidate obligations incurred. The first such area to be studied was the Delta Area in Millard County. This area was selected for this study because of the pressing need for more detailed and wider information than was available to either the farmers or the bondholders and because available facts based on careful study might aid in achieving fairer settlements. These data might also assist other areas in eliminating wastes which multiply in hastily planned undertakings

Sorghum ergot - a sticky disease problem in southern Africa

Ergot disease of sorghum is not new to Africa - the causal pathogen, Claviceps africana Frederickson, Mantle, and de Milliano was first recorded in Kenya as far back as 1923. However, ergot disease only began to gain recognition as a potential problem in sorghum production in the 1960s, when all the A-lines in Nigeria's national breeding program became infected, to the near complete exclusion of seed production (Futrell and Webster 1965)

Potential Use of Benomyl for Control of Ergot (Claviceps africana) in Sorghum A-lines in Zimbabwe

In the absence of a successful practice for the control of ergot (caused by C. africana) on sorghum A-lines (male-steriles) in Zimbabwe, 2 fungicides, benomyl as Benlate and thiram, were tested in greenhouse and field experiments conducted at the Matopos and Henderson Research Stations, Zimbabwe in 1993. Fungicides were either applied to sorghum panicles singly, at concentrations of 0.1 or 0.2% a.i., or combined in mixtures at 0.1% a.i. each. Fungicides were applied before inoculation at heading or stigma exsertion or after disease became visible. Treatment with either benomyl or thiram was ineffective if applied when disease first became visible. A significant reduction in initial disease severity, rate of disease increase and final disease severity was achieved with 1 application of benomyl at 0.2% a.i. at heading or stigma exsertion. At the concentrations tested benomyl and thiram did not reduce seed-set in R- (restorer) lines

Pearl Millet as an Alternate Host of the Sorghum Ergot Pathogen, Claviceps africana

The infectivity of C. africana on pearl millet (Pennisetum glaucum) lines in Africa was studied. C. africana consistently gave 100% disease incidence on male-sterile sorghum in experiments undertaken in Zimbabwe. C. fusiformis established disease with moderate incidence on most but not all lines tested. In contrast, C. africana established a parasitic association with all the pearl millet lines tested, with incidence as high as 23% in ICMSR 260, the genotype that also supported the highest incidence with C. fusiformis. However, the disease severities were always low, between 1 and 5%. All infections on pearl millet were verified as the sphacelial stage by virtue of their conidial characteristics. After 1 passage through a pearl millet host, C. africana did not apparently become more infectious on this host

Matroid and Knapsack Center Problems

In the classic $k$-center problem, we are given a metric graph, and the objective is to open $k$ nodes as centers such that the maximum distance from any vertex to its closest center is minimized. In this paper, we consider two important generalizations of $k$-center, the matroid center problem and the knapsack center problem. Both problems are motivated by recent content distribution network applications. Our contributions can be summarized as follows: 1. We consider the matroid center problem in which the centers are required to form an independent set of a given matroid. We show this problem is NP-hard even on a line. We present a 3-approximation algorithm for the problem on general metrics. We also consider the outlier version of the problem where a given number of vertices can be excluded as the outliers from the solution. We present a 7-approximation for the outlier version. 2. We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s). It is known that the knapsack center problem with a single knapsack constraint admits a 3-approximation. However, when there are at least two knapsack constraints, we show this problem is not approximable at all. To complement the hardness result, we present a polynomial time algorithm that gives a 3-approximate solution such that one knapsack constraint is satisfied and the others may be violated by at most a factor of $1+\epsilon$. We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by $1+\epsilon$.Comment: A preliminary version of this paper is accepted to IPCO 201