An O(log⁡n)O(\log n)-approximation for the Set Cover Problem with Set Ownership

In highly distributed Internet measurement systems distributed agents periodically measure the Internet using a tool called {\tt traceroute}, which discovers a path in the network graph. Each agent performs many traceroute measurement to a set of destinations in the network, and thus reveals a portion of the Internet graph as it is seen from the agent locations. In every period we need to check whether previously discovered edges still exist in this period, a process termed {\em validation}. For this end we maintain a database of all the different measurements performed by each agent. Our aim is to be able to {\em validate} the existence of all previously discovered edges in the minimum possible time. In this work we formulate the validation problem as a generalization of the well know set cover problem. We reduce the set cover problem to the validation problem, thus proving that the validation problem is ${\cal NP}$-hard. We present a $O(\log n)$-approximation algorithm to the validation problem, where $n$ in the number of edges that need to be validated. We also show that unless ${\cal P = NP}$ the approximation ratio of the validation problem is $\Omega(\log n)$

Time-dependent coupled-cluster method for atomic nuclei

We study time-dependent coupled-cluster theory in the framework of nuclear physics. Based on Kvaal's bi-variational formulation of this method [S. Kvaal, arXiv:1201.5548], we explicitly demonstrate that observables that commute with the Hamiltonian are conserved under time evolution. We explore the role of the energy and of the similarity-transformed Hamiltonian under real and imaginary time evolution and relate the latter to similarity renormalization group transformations. Proof-of-principle computations of He-4 and O-16 in small model spaces, and computations of the Lipkin model illustrate the capabilities of the method.Comment: 10 pages, 9 pdf figure

Shortcuts through Colocation Facilities

Network overlays, running on top of the existing Internet substrate, are of perennial value to Internet end-users in the context of, e.g., real-time applications. Such overlays can employ traffic relays to yield path latencies lower than the direct paths, a phenomenon known as Triangle Inequality Violation (TIV). Past studies identify the opportunities of reducing latency using TIVs. However, they do not investigate the gains of strategically selecting relays in Colocation Facilities (Colos). In this work, we answer the following questions: (i) how Colo-hosted relays compare with other relays as well as with the direct Internet, in terms of latency (RTT) reductions; (ii) what are the best locations for placing the relays to yield these reductions. To this end, we conduct a large-scale one-month measurement of inter-domain paths between RIPE Atlas (RA) nodes as endpoints, located at eyeball networks. We employ as relays Planetlab nodes, other RA nodes, and machines in Colos. We examine the RTTs of the overlay paths obtained via the selected relays, as well as the direct paths. We find that Colo-based relays perform the best and can achieve latency reductions against direct paths, ranging from a few to 100s of milliseconds, in 76% of the total cases; 75% (58% of total cases) of these reductions require only 10 relays in 6 large Colos.Comment: In Proceedings of the ACM Internet Measurement Conference (IMC '17), London, GB, 201