Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some Sidon spaces by using primitive elements and the roots of some irreducible polynomials over finite fields. Let q be a prime power, k, m, n be three positive integers and $ ho= lceil rac{m}{2k} ceil-1$, $ heta= lceil rac{n}{2m} ceil-1$. Based on these Sidon spaces and the union of some Sidon spaces, new cyclic subspace codes with size $rac{3(q^{n}-1)}{q-1}$ and $rac{ heta ho q^{k}(q^{n}-1)}{q-1}$ are obtained. The size of these codes is lager compared to the known constructions from [14] and [10].

Robustness of complex networks is an essential subject for improving their performance when vertices or links are removed due to potential threats. In recent years, significant advancements have been achieved in this field by many researchers. In this paper we show an overview from a novel statistic perspective. We present a brief review about complex networks at first including 2 primary network models, 12 popular attack strategies and the most convincing network robustness metrics. Then, we focus on the correlations of 12 attack strategies with each other, and the difference of the correlations from one network model to the other. We are also curious about the robustness of networks when vertices are removed according to different attack strategies and the difference of robustness from one network model to the other. Our aim is to observe the correlation mechanism of centralities for distinct network models, and compare the network robustness when different centralities are applied as attacking directors to distinct network models. What inspires us is that maybe we can find a paradigm that combines several high-destructive attack strategies to find the optimal strategy based on the deep learning framework.

Random network topologies have been proposed as a low-latency network for parallel computers. Although multicast is a common collective-communication operation, multicast algorithms each of which consists of a large number of unicasts are not well optimized for random network topologies. In this study, we firstly apply a two-opt algorithm for building efficient multicast on random network topologies. The two-opt algorithm creates a skilled ordered list of visiting nodes to minimize the total path hops or the total possible contention counts of unicasts that form the target multicast. We secondly extend to apply the two-opt algorithm for the other collective-communication operations, e.g., allreduce and allgather. The SimGrid discrete-event simulation results show that the two-opt multicast outperforms that in typical MPI implementation by up to 22% of the execution time of an MPI program that repeats the MPI_Bcast function. The two-opt allreduce and the two-opt allgather operations also improve by up to 15% and 14% the execution time when compared to those used in typical MPI implementations, respectively.

Most large-scale Peer-to-Peer (P2P) live streaming systems are constructed as a mesh structure, which can provide robustness in the dynamic P2P environment. The pull scheduling algorithm is widely used in this mesh structure, which degrades the performance of the entire system. Recently, network coding was introduced in mesh P2P streaming systems to improve the performance, which makes the push strategy feasible. One of the most famous scheduling algorithms based on network coding is R2, with a random push strategy. Although R2 has achieved some success, the push scheduling strategy still lacks a theoretical model and optimal solution. In this paper, we propose a novel optimal pull-push scheduling algorithm based on network coding, which consists of two stages: the initial pull stage and the push stage. The main contributions of this paper are: 1) we put forward a theoretical analysis model that considers the scarcity and timeliness of segments; 2) we formulate the push scheduling problem to be a global optimization problem and decompose it into local optimization problems on individual peers; 3) we introduce some rules to transform the local optimization problem into a classical min-cost optimization problem for solving it; 4) We combine the pull strategy with the push strategy and systematically realize our scheduling algorithm. Simulation results demonstrate that decode delay, decode ratio and redundant fraction of the P2P streaming system with our algorithm can be significantly improved, without losing throughput and increasing overhead.

In network coding, for the case that the network topology is unknown completely, random linear network coding has been proposed as an acceptable coding technique. In this paper, we define average failure probability of random linear network coding in order to characterize the performance of random network coding, and then analyze this failure probability for different known topological information of network. We obtain several upper bounds on the failure probabilities, and further show that, for some networks, these upper bounds are tight or asymptotically tight. Moreover, if the more topological information of the network is utilized, the better upper bounds are acquired.

We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give estimates on the time complexity and the required symbol size of the proposed algorithm. We also estimate the probability of a random choice of local encoding vectors by all intermediate nodes giving a network error-correcting codes attaining the Singleton bound. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors.

A mesh spiral network (MSnet) and a mesh random (MRnet) are proposed. The MSnet consists of the 2-D torus and bypass links that keep the degree at six. The MRnet consists of the 2-D torus and random bypass links that keep the degree at six. The diameter and the average distance are calculated by using a computer program. The cost of the MSnet is slightly higher than that of the de Bruijn graph, and is about the same as the Star graph. The cost of the MRnet is better than that of the de Bruijn graph. The MSnet is proven to be maximally fault-tolerant. The upper bound of the MRnet size is also discussed.

One of the important properties of multihop network is the mean internodal distance to evaluate the transmission delay, and the connective semi-random network achieves smaller mean internodal distance than other networks. However, the results are shown only by computer simulation and no theoretical analysis is investigated. Moreover, the network connective probability of the connective semi-random network is relatively small. In this paper, we propose the restricted connective semi-random network whose network connective probability is larger than that of the conventional connective semi-random network. And we theoretically analyze the mean internodal distance and the network connective probability of these two networks. It is shown that if the restriction is loose, the mean internodal distance of our model is almost the same as that of the conventional model, whereas the network connective probability of our model is larger than that of the conventional model. Moreover, the theoretical analyzed results of the mean internodal distance agree well with the simulated results in the conventional model and our model with small restriction.