Brief Announcement: On Connectivity in the Broadcast Congested Clique

Recently, very fast deterministic and randomized algorithms have been obtained for connectivity and minimum spanning tree in the unicast congested clique. In contrast, no solution faster than a simple parallel implementation of the Boruvka\u27s algorithm has been known for both problems in the broadcast congested clique. In this announcement, we present the first sub-logarithmic deterministic algorithm for connected components in the broadcast congested clique

A Deterministic Algorithm for the MST Problem in Constant Rounds of Congested Clique

In this paper, we show that the Minimum Spanning Tree problem can be solved \emph{deterministically}, in $\mathcal{O}(1)$ rounds of the $\mathsf{Congested}$ $\mathsf{Clique}$ model. In the $\mathsf{Congested}$ $\mathsf{Clique}$ model, there are $n$ players that perform computation in synchronous rounds. Each round consist of a phase of local computation and a phase of communication, in which each pair of players is allowed to exchange $\mathcal{O}(\log n)$ bit messages. The studies of this model began with the MST problem: in the paper by Lotker et al.[SPAA'03, SICOMP'05] that defines the $\mathsf{Congested}$ $\mathsf{Clique}$ model the authors give a deterministic $\mathcal{O}(\log \log n)$ round algorithm that improved over a trivial $\mathcal{O}(\log n)$ round adaptation of Bor\r{u}vka's algorithm. There was a sequence of gradual improvements to this result: an $\mathcal{O}(\log \log \log n)$ round algorithm by Hegeman et al. [PODC'15], an $\mathcal{O}(\log^* n)$ round algorithm by Ghaffari and Parter, [PODC'16] and an $\mathcal{O}(1)$ round algorithm by Jurdzi\'nski and Nowicki, [SODA'18], but all those algorithms were randomized, which left the question about the existence of any deterministic $o(\log \log n)$ round algorithms for the Minimum Spanning Tree problem open. Our result resolves this question and establishes that $\mathcal{O}(1)$ rounds is enough to solve the MST problem in the $\mathsf{Congested}$ $\mathsf{Clique}$ model, even if we are not allowed to use any randomness. Furthermore, the amount of communication needed by the algorithm makes it applicable to some variants of the $\mathsf{MPC}$ model

Poland’s problems regarding the adaptation of the system of environmental law in the light of judgment of the Court of Justice of 21 June 2018

Poland’s problems regarding the adaptation of the system of environmental law in the light of judgment of the Court  of Justice of 21 June 201

Faster Algorithms for Edge Connectivity via Random 22-Out Contractions

We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We demonstrate the power of our new approach by obtaining better algorithms for sequential, distributed, and parallel models of computation. Our end results include the following randomized algorithms for computing edge connectivity with high probability: -- Two sequential algorithms with complexities $O(m \log n)$ and $O(m+n \log^3 n)$. These improve on a long line of developments including a celebrated $O(m \log^3 n)$ algorithm of Karger [STOC'96] and the state of the art $O(m \log^2 n (\log\log n)^2)$ algorithm of Henzinger et al. [SODA'17]. Moreover, our $O(m+n \log^3 n)$ algorithm is optimal whenever $m = \Omega(n \log^3 n)$. Within our new time bounds, whp, we can also construct the cactus representation of all minimal cuts. -- An $\~O(n^{0.8} D^{0.2} + n^{0.9})$ round distributed algorithm, where D denotes the graph diameter. This improves substantially on a recent breakthrough of Daga et al. [STOC'19], which achieved a round complexity of $\~O(n^{1-1/353}D^{1/353} + n^{1-1/706})$, hence providing the first sublinear distributed algorithm for exactly computing the edge connectivity. -- The first $O(1)$ round algorithm for the massively parallel computation setting with linear memory per machine.Comment: algorithms and data structures, graph algorithms, edge connectivity, out-contractions, randomized algorithms, distributed algorithms, massively parallel computatio

Dispersal in a metapopulation of the critically endangered Danube Clouded Yellow butterfly Colias myrmidone : implications for conservation

Colias myrmidone has suffered a dramatic decline in Europe, and now its occurrence is restricted to just a few countries. We investigated one of the last viable metapopulations (Knyszyn Forest, NE Poland), where the butterfly is almost completely dependent on forestry, inhabiting some clearings and young tree plantations rich in larval food plants (Chamaecytisus ruthenicus) and nectar resources. Intensive mark-recapture studies were performed in 2017 on eight occupied patches separated by 0.5-5km. The overall population size of imagoes in the second brood was calculated at about 750 individuals. Sex ratio was shown to be well-balanced and average residency was estimated at 5.6 days. Dispersal occurred mostly between neighbouring patches, and isolation of patches contributed to the high mortality of emigrants. The average distance covered during dispersal was significantly higher for males. However, females left small patches much more readily than males. These patches were probably used only as stepping stone' sites in dispersal. Restricted dispersal could be related to barriers created by forest stands but it is also not excluded that individuals living in an isolated metapopulation become increasingly sedentary and our results are an early warning sign. The most distant local population was clearly isolated, with hardly any immigration from the other populations. To maintain a network of more stable habitat patches some clearings should be left deforested and appropriately managed. However this goal is difficult to achieve under the current forestry rules and therefore (re)creation of habitats on other available open areas should be considered

The Relationship between Trabecular Bone Structure Modeling Methods and the Elastic Modulus as Calculated by FEM

Trabecular bone cores were collected from the femoral head at the time of surgery (hip arthroplasty). Investigated were 42 specimens, from patients with osteoporosis and coxarthrosis. The cores were scanned used computer microtomography (microCT) system at an isotropic spatial resolution of 36 microns. Image stacks were converted to finite element models via a bone voxel-to-element algorithm. The apparent modulus was calculated based on the assumptions that for the elastic properties, E = 10 MPa and ν = 0.3. The compressive deformation as calculated by finite elements (FE) analysis was 0.8%. The models were coarsened to effectively change the resolution or voxel size (from 72 microns to 288 microns or from 72 microns to 1080 microns). The aim of our study is to determine how an increase in the distance between scans changes the elastic properties as calculated by FE models. We tried to find a border value voxel size at which the module values were possible to calculate. As the voxel size increased, the mean voxel volume increased and the FEA-derived apparent modulus decreased. The slope of voxel size versus modulus relationship correlated with several architectural indices of trabecular bone

A hybrid-mesh solutionfor coverage issues in WiMAX metropolitan area networks, Journal of Telecommunications and Information Technology, 2008, nr 1

The new WiMAX technology offers several advantages over the currently available (GSMor UMTS-based) solutions. It is a cost effective, evolving, and robust technology providing quality of service guarantees, high reliability, wide cov- erage and non-line-of-sight (NLOS) transmission capabilities. All these features make it particularly suitable for densely populated urban environments. In this paper we discuss the design and implementation difficulties concerning network coverage discovered in a test-bed implementation of WiMAX. We point out the presence of unexpected “white spots” in the coverage, which are not inherently characteristic of the WiMAX concept. As a possible remedy to this significant drawback of the otherwise very promising technology, we consider reconfigurable mesh organization of WiMAX base stations. We also suggest directions for further development of this kind of network operation, partly based on our practical experience. Despite the clear advantages of the mesh mode in WiMAX networks, its development is currently at an early stage, due to the high complexity of the necessary mechanisms. In this situation, we propose an original, much simpler solution: the so-called support-mesh mode