Consider the problem of discovering (or verifying) the edges and nonedges of a network, modelled as a connected undirected graph, using a minimum number of queries. A query at a vertex v discovers (or verifies) all edges and nonedges whose endpoints have different distance from v. In the network discovery problem, the edges and non-edges are initially unknown, and the algorithm must select the next query based only on the results of previous queries. We study the problem using competitive analysis and give a randomized on-line algorithm with competitive ratio O( √ n log n) for graphs with n vertices. We also show that no deterministic algorithm can have competitive ratio better than 3. In the network verification problem, the graph is known in advance and the goal is to compute a minimum number of queries that verify all edges and non-edges. This problem has previously been studied as the problem of placing landmarks in graphs or determining the metric dimension of a graph. We show that there is no approximation algorithm for this problem with ratio o(log n) unless P = N P. Furthermore, we prove that the optimal number of queries for d-dimensional hypercubes is Θ(d/ log d).

Abstract-

For a given number L, an L-length-bounded edge-cut (node-cut, resp.) in a graph G with source s and sink t is a set C of edges (nodes, resp.) such that no s-t-path of length at most L remains in the graph after removing the edges (nodes, resp.) in C. An L-length-bounded flow is a flow that can be decomposed into flow paths of length at most L. In contrast to the classical flow theory, we describe instances for which the minimum L-length-bounded edge-cut (node-cut, resp.) is Θ(n 2/3 )-times (Θ( √ n)-times, resp.) larger than the maximum L-length-bounded flow, where n denotes the number of nodes; this is the worst case. We show that the minimum length-bounded cut problem is N P-hard to approximate within a factor of 1.1377 for L ≥ 5 in the case of nodecuts and for L ≥ 4 in the case of edge-cuts. We also describe algorithms with approximation ratio O(min{L, n/L}) ⊆ O( √ n) in the node case and O(min{L, n 2 /L 2 , √ m}) ⊆ O(n 2/3 ) in the edge case, where m denotes the number of edges. Concerning L-length-bounded flows, we show that in graphs with unit-capacities and general edge lengths it is N P-complete to decide whether there is a fractional length-bounded flow of a given value. We analyze the structure of optimal solutions and present further complexity results.

Column-oriented database systems have been a real game changer for the industry in recent years. Highly tuned and performant systems have evolved that provide users with the possibility of answering ad hoc queries over large datasets in an interactive manner.In this paper we present the column-oriented datastore developed as one of the central components of PowerDrill 1 . It combines the advantages of columnar data layout with other known techniques (such as using composite range partitions) and extensive algorithmic engineering on key data structures. The main goal of the latter being to reduce the main memory footprint and to increase the efficiency in processing typical user queries. In this combination we achieve large speed-ups. These enable a highly interactive Web UI where it is common that a single mouse click leads to processing a trillion values in the underlying dataset.

This is the second of two companion papers that describe the development of the RemoveDEBRIS space mission. This second article describes the in-orbit operations that were performed to demonstrate technologies to be used for the active removal of space debris, whereas the first paper described the development of the satellite's hardware. The RemoveDebris mission has been the world's first Active Debris Removal (ADR) mission to successfully demonstrate, in orbit, some cost effective technologies, including net and harpoon capture; and elements of the whole sequence of operations, like the visionbased navigation. The satellite was launched the 2 nd of April 2018, to the International Space Station (ISS) and from there, on the 20 th of June 2018, was deployed via the NanoRacks Kaber system into an orbit of 405 km altitude. During the mission, two 2U CubeSats have been released by the mothercraft platform as artificial debris targets, to demonstrate net capture and cameras to be used for vision based navigation. Harpoon capture has been demonstrated by deploying a target and then firing at it a harpoon tethered to the platform. The various phases of the missions have been monitored using relevant telemetry and video cameras, and this paper reports the results of the various demonstrations.