scholarly journals Computation with No Memory, and Rearrangeable Multicast Networks

2014 ◽  
Vol Vol. 16 no. 1 ◽  
Author(s):  
Emeric Gioan ◽  
Serge Burckel ◽  
Emmanuel Thomé
Keyword(s):  
Multicast Routing ◽  
Close Relation ◽  
Linear Mapping ◽  
Maximal Length ◽  
Arbitrary Mapping ◽  
Matrix Decompositions ◽  
Multicast Networks ◽  
International Audience ◽  
Routing Methods

International audience We investigate the computation of mappings from a set S^n to itself with "in situ programs", that is using no extra variables than the input, and performing modifications of one component at a time, hence using no extra memory. In this paper, we survey this problem introduced in previous papers by the authors, we detail its close relation with rearrangeable multicast networks, and we provide new results for both viewpoints. A bijective mapping can be computed by 2n-1 component modifications, that is by a program of length 2n-1, a result equivalent to the rearrangeability of the concatenation of two reversed butterfly networks. For a general arbitrary mapping, we give two methods to build a program with maximal length 4n-3. Equivalently, this yields rearrangeable multicast routing methods for the network formed by four successive butterflies with alternating reversions. The first method is available for any set S and practically equivalent to a known method in network theory. The second method, a refinment of the first, described when |S| is a power of 2, is new and allows more flexibility than the known method. For a linear mapping, when S is any field, or a quotient of an Euclidean domain (e.g Z/sZ for any integer s), we build a program with maximal length 2n-1. In this case the assignments are also linear, thereby particularly efficient from the algorithmic viewpoint, and giving moreover directly a program for the inverse when it exists. This yields also a new result on matrix decompositions, and a new result on the multicast properties of two successive reversed butterflies. Results of this flavour were known only for the boolean field Z/2Z.

ON THE DESIGN OF DEADLOCK-FREE ADAPTIVE MULTICAST ROUTING ALGORITHMS

1993 ◽  
Vol 03 (04) ◽  
pp. 321-333 ◽  
Author(s):  
JOSÉ DUATO
Keyword(s):  
Multicast Routing ◽  
Routing Algorithm ◽  
Sufficient Conditions ◽  
Adaptive Routing ◽  
Routing Algorithms ◽  
Multicast Communication ◽  
Adaptive Multicast ◽  
Routing Methods ◽  
Wormhole Networks ◽  
Additional Channel

Multicast communication refers to the delivery of the same message from one source node to an arbitrary number of destination nodes. Two multicast wormhole routing methods have been presented in [13] for multicomputers with 2D-mesh and hypercube topologies. Also, a theory for the design of deadlock-free adaptive routing algorithms for wormhole networks has been proposed in [7, 8]. This theory supplies the sufficient conditions for an adaptive routing algorithm to be deadlock-free, even when there are cyclic dependencies between channels. This paper analyses the additional channel dependencies produced by multicast routing algorithms on wormhole networks. Then, the theory proposed in [7, 8] is extended by considering them. As an example, the multicast routing algorithms presented in [13] are extended, taking advantage of the alternative paths offered by the network.

scholarly journals The facial weak order in finite Coxeter groups

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Aram Dermenjian ◽  
Christophe Hohlweg ◽  
Vincent Pilaud
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Geometric Interpretation ◽  
Weak Order ◽  
Maximal Length ◽  
Lattice Congruence ◽  
Finite Coxeter Group ◽  
International Audience

International audience We investigate a poset structure that extends the weak order on a finite Coxeter group W to the set of all faces of the permutahedron of W. We call this order the facial weak order. We first provide two alternative characterizations of this poset: a first one, geometric, that generalizes the notion of inversion sets of roots, and a second one, combinatorial, that uses comparisons of the minimal and maximal length representatives of the cosets. These characterizations are then used to show that the facial weak order is in fact a lattice, generalizing a well-known result of A. Bjo ̈rner for the classical weak order. Finally, we show that any lattice congruence of the classical weak order induces a lattice congruence of the facial weak order, and we give a geometric interpretation of its classes.

scholarly journals A Two-Layered Shared Tree Multicast Routing Algorithm for Software Defined Hybrid Satellite-Terrestrial Communication Networks

2021 ◽  
Vol 2 ◽  
Author(s):  
Jiayan Xiong ◽  
Zhen Xu ◽  
Zhiqi Dai
Keyword(s):  
Congestion Control ◽  
Multicast Routing ◽  
Routing Algorithm ◽  
Load Factor ◽  
Multicast Group ◽  
Multicast Networks ◽  
Network Bandwidth ◽  
Dynamic Multicast ◽  
Terrestrial Networks ◽  
Shared Tree

Dynamic routing and congestion control are two major problems in software-defined hybrid satellite-terrestrial multicast networks research. Due to terrestrial users being allowed to join or leave the multicast group at any time and the differences between the satellite and the terrestrial networks, many multicast routing algorithms reroute rapidly and thus increase the rerouting overheads. Meanwhile, the congestion ratio is increased by some hot nodes of satellite-terrestrial link transmission paths. This paper focuses on rerouting overheads and congestion problems in satellite-terrestrial multicast networks. We present a satellite-terrestrial network architecture with the Software-Defined Networking (SDN) features to offer dynamic multicast services for terrestrial users. A Two-Layered Shared Tree Multicast (TSTM) routing algorithm is proposed to achieve efficient dynamic multicast group management, address the trade-off between bandwidth consumption and rerouting overheads. The algorithm also implements congestion control by using a load factor to reflect on the global network bandwidth usage in routing calculations. This algorithm balances the rerouting frequencies of satellite and terrestrial networks to decrease the rerouting overheads and also reduces the network congestion ratio. The simulation shows TSTM decreases rerouting cost, user time delay, and node congestion ratio compared with the locality-aware multicast approach (LAMA).

UNITED KINGDOM IN-SITU BURN TRIALS, LOWESTOFT, 1996

1997 ◽  
Vol 1997 (1) ◽  
pp. 131-136
Author(s):  
James Thornborough
Keyword(s):  
United Kingdom ◽  
Oil Spill ◽  
Worker Safety ◽  
Oil Analysis ◽  
Air Samples ◽  
The United Kingdom ◽  
International Audience ◽  
Oil Spill Response ◽  
Atmospheric Sampling

ABSTRACT On June 12, 1996, in a location 40 miles offshore of Lowestoft, an international audience gathered to watch Oil Spill Response Limited conduct the first controlled in-situ burn (ISB) in the United Kingdom. Two burns were completed using a response-prepared ISB system. The first burn involved fresh crude oil and was lit with a hand-held igniter using a standard gel mix. The second burn involved an emulsified crude and was lit using the Helitorch and an emulsion-breaking ignition mix. The trials were performed with the aim of determining operational practicalities under realistic conditions when responding to a weathered oil situation in an offshore location. Peripheral attention was paid to atmospheric sampling, except that air samples were collected aboard the main deployment vessel to assess worker safety. Oil analysis was carried out primarily to assess the values of the emulsion that was left as residue.

scholarly journals Minimal Recurrent Configurations of Chip Firing Games and Directed Acyclic Graphs

2010 ◽  
Vol DMTCS Proceedings vol. AL,... (Proceedings) ◽  
Author(s):  
Matthias Schulz
Keyword(s):  
Lower Bound ◽  
Close Relation ◽  
Directed Acyclic Graphs ◽  
Sandpile Model ◽  
Abelian Sandpile Model ◽  
Acyclic Graphs ◽  
Abelian Sandpile ◽  
Chip Firing ◽  
International Audience

International audience We discuss a very close relation between minimal recurrent configurations of Chip Firing Games and Directed Acyclic Graphs and demonstrate the usefulness of this relation by giving a lower bound for the number of minimal recurrent configurations of the Abelian Sandpile Model as well as a lower bound for the number of firings which are caused by the addition of two recurrent configurations on particular graphs.

scholarly journals Computation of L_⊕ for several cubic Pisot numbers

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Julien Bernat
Keyword(s):  
Central Symmetry ◽  
Maximal Length ◽  
Pisot Numbers ◽  
International Audience ◽  
Integer Base

International audience In this article, we are dealing with β-numeration, which is a generalization of numeration in a non-integer base. We consider the class of simple Parry numbers such that dβ(1) = 0.k1d-1 kd with d ∈ ℕ, d ≥ 2 and k1 ≥ kd ≥ 1. We prove that these elements define Rauzy fractals that are stable under a central symmetry. We use this result to compute, for several cases of cubic Pisot units, the maximal length among the lengths of the finite β-fractional parts of sums of two β-integers, denoted by L_⊕. In particular, we prove that L_⊕ = 5 in the Tribonacci case.

scholarly journals Slipped capital femoral epiphysis: an epidemiological Nationwide study in Italy from 2001 to 2015

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Umile Giuseppe Longo ◽  
Rocco Papalia ◽  
Sergio De Salvatore ◽  
Laura Ruzzini ◽  
Vincenzo Candela ◽  
...  
Keyword(s):  
Slipped Capital Femoral Epiphysis ◽  
Statistical Prediction ◽  
Stable Form ◽  
Italian Population ◽  
Level Of Evidence ◽  
Hip Disease ◽  
International Audience ◽  
The Difference ◽  
In Situ Pinning

Abstract Background Slipped capital femoral epiphysis (epiphysiolysis of the femoral head, SCFE) is the most common pediatric hip disease in 10–14 years old children. The most used procedure to correct a stable form of SCFE is in situ pinning. Instead, the proper treatment for unstable forms is controversial. The first purpose of this study was to estimate annual admissions for SCFE in Italian patients from 2001 to 2015, basing on the hospitalization reports. The second aim was to assess the difference between regions regarding SCFE procedures. Lastly, a statistical prediction of the volume of SCFE procedures performed in Italy based on data from 2001 to 2015 was performed. Methods Data of this study were collected from the National Hospital Discharge Reports (SDO) reported at the Italian Ministry of Health regarding the years of this paper. The yearly number of hospital admission for SCFE, the percentage of males and females, the average age, days of hospitalization, primary diagnoses and primary procedures in the whole Italian population were calculated using descriptive statistical analyses. Results From 2001 to 2015, 4893 hospitalizations for SCFE were recorded in Italy, with a mean incidence of 2.9 (cases/100.000 inhabitants). The majority of patients treated by SCFE were males (70.6%). Conclusion National health statistics for SCFE are attractive for an international audience, as different approaches to screening are reported between countries. These differences allow comparing outcomes internationally. Moreover, sharing national statistics and correlating those to other countries protocols, could be helpful to compare outcomes for different procedures internationally. However, further studies are required to understand the specific reasons for regional variation for SCFE procedures in Italy. Level of evidence III

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