35 research outputs found
Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree
We present algorithms for distributed verification and silent-stabilization
of a DFS(Depth First Search) spanning tree of a connected network. Computing
and maintaining such a DFS tree is an important task, e.g., for constructing
efficient routing schemes. Our algorithm improves upon previous work in various
ways. Comparable previous work has space and time complexities of bits per node and respectively, where is the highest
degree of a node, is the number of nodes and is the diameter of the
network. In contrast, our algorithm has a space complexity of bits
per node, which is optimal for silent-stabilizing spanning trees and runs in
time. In addition, our solution is modular since it utilizes the
distributed verification algorithm as an independent subtask of the overall
solution. It is possible to use the verification algorithm as a stand alone
task or as a subtask in another algorithm. To demonstrate the simplicity of
constructing efficient DFS algorithms using the modular approach, We also
present a (non-sielnt) self-stabilizing DFS token circulation algorithm for
general networks based on our silent-stabilizing DFS tree. The complexities of
this token circulation algorithm are comparable to the known ones
Mass calibration of DES Year-3 clusters via SPT-3G CMB cluster lensing
We measure the stacked lensing signal in the direction of galaxy clusters in the Dark Energy Survey Year 3 (DES Y3) redMaPPer sample, using cosmic microwave background (CMB) temperature data from SPT-3G, the third-generation CMB camera on the South Pole Telescope (SPT). Here, we estimate the lensing signal using temperature maps constructed from the initial 2 years of data from the SPT-3G 'Main' survey, covering 1500 deg2 of the Southern sky. We then use this lensing signal as a proxy for the mean cluster mass of the DES sample. The thermal Sunyaev-Zel'dovich (tSZ) signal, which can contaminate the lensing signal if not addressed, is isolated and removed from the data before obtaining the mass measurement. In this work, we employ three versions of the redMaPPer catalogue: a Flux-Limited sample containing 8865 clusters, a Volume-Limited sample with 5391 clusters, and a Volume&Redshift-Limited sample with 4450 clusters. For the three samples, we detect the CMB lensing signal at a significance of 12.4σ, 10.5σ and 10.2σ and find the mean cluster masses to be M 200m = 1.66±0.13 [stat.]± 0.03 [sys.], 1.97±0.18 [stat.]± 0.05 [sys.], and 2.11±0.20 [stat.]± 0.05 [sys.]×1014 M⊙, respectively. This is a factor of ∼ 2 improvement relative to the precision of measurements with previous generations of SPT surveys and the most constraining cluster mass measurements using CMB cluster lensing to date. Overall, we find no significant tensions between our results and masses given by redMaPPer mass-richness scaling relations of previous works, which were calibrated using CMB cluster lensing, optical weak lensing, and velocity dispersion measurements from various combinations of DES, SDSS and Planck data. We then divide our sample into 3 redshift and 3 richness bins, finding no significant discrepancies with optical weak-lensing calibrated masses in these bins. We forecast a 5.7% constraint on the mean cluster mass of the DES Y3 sample with the complete SPT-3G surveys when using both temperature and polarization data and including an additional ∼ 1400 deg2 of observations from the 'Extended' SPT-3G survey