Lower Bound on de Bruijn Graphs Out-degree for Lower Traffic Load in Peer-to-peer Networks

Designers search for N-nodes peer-to-peer networks that can have O （1） out-degree with O （log2 N） average distance. Peer-to-peer schemes based on de Bruijn graphs are found to meet this requirement. By defining average load to evaluate the traffic load in a network, we show that in order to decrease the average load, the average distance of a network should decrease while the out-degree should increase. Especially, given out-degree k and N nodes, peer-to-peer schemes based on de Bruijn graphs have lower average load than other existing systems. The out-degree k of de Bruijn graphs should not be O（1） but should satisfy a lower bound described by an inequality κ^κ≥N^2, to ensure that the average load in peer-to-peer schemes based on de Bruijn graphs will not exceed that in Chord system.

Degree sequences of k-multi-hypertournaments

Let n and k（n ≥ k 〉 1） be two non-negative integers.A k-multi-hypertournament on n vertices is a pair（V,A）,where V is a set of vertices with ｜V｜=n,and A is a set of k-tuples of vertices,called arcs,such that for any k-subset S of V,A contains at least one（at most k!） of the k! k-tuples whose entries belong to S.The necessary and suffcient conditions for a non-decreasing sequence of non-negative integers to be the out-degree sequence（in-degree sequence） of some k-multi-hypertournament are given.

Time optimization for workflow scheduling based on the combination of task attributes

In order to reduce the scheduling makespan of a workflow,three list scheduling algorithms,namely,level and out-degree earliest-finish-time(LOEFT),level heterogeneous selection value(LHSV),and heterogeneous priority earliest-finish-time(HPEFT)are proposed.The main idea hidden behind these algorithms is to adopt task depth,combined with task out-degree for the accurate analysis of task prioritization and precise processor allocation to achieve time optimization.Each algorithm is divided into three stages:task levelization,task prioritization,and processor allocation.In task levelization,the workflow is divided into several independent task sets on the basis of task depth.In task prioritization,the heterogeneous priority ranking value(HPRV)of the task is calculated using task out-degree,and a non-increasing ranking queue is generated on the basis of HPRV.In processor allocation,the sorted tasks are assigned one by one to the processor to minimize makespan and complete the task-processor mapping.Simulation experiments through practical applications and stochastic workflows confirm that the three algorithms can effectively shorten the workflow makespan,and the LOEFT algorithm performs the best,and it can be concluded that task depth combined with out-degree is an effective means of reducing completion time.

Structure and Connectivity Analysis of Financial Complex System Based on G-Causality Network

The recent financial crisis highlights the inherent weaknesses of the financial market. To explore the mechanism that maintains the financial market as a system, we study the interactions of U.S. financial market from the network perspective. Applied with conditional Granger causality network analysis, network density, in-degree and out-degree rankings are important indicators to analyze the conditional causal relationships among financial agents, and further to assess the stability of U.S. financial systems. It is found that the topological structure of G-causality network in U.S. financial market changed in different stages over the last decade, especially during the recent global financial crisis. Network density of the G-causality model is much higher during the period of 2007-2009 crisis stage, and it reaches the peak value in 2008, the most turbulent time in the crisis. Ranked by in-degrees and out-degrees, insurance companies are listed in the top of 68 financial institutions during the crisis. They act as the hubs which are more easily influenced by other financial institutions and simultaneously influence others during the global financial disturbance.

On Disjoint Cycles of the Same Length in Tournaments

A tournament is an orientation of the complete graph.Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application.Tournaments provide a model of the statistical technique called the method of paired comparisons and they have also been studied in connection with sociometric relations in small groups.In this paper,we investigate disjoint cycles of the same length in tournaments.In 2010,Lichiardopol conjectured that for given integers l≥3 and k≥1,any tournament with minimum out-degree at least(l-1)k-1 contains k disjoint l-cycles,where an l-cycle is a cycle of order l.Bang-Jensen et al.verified the conjecture for l=3 and Ma et al.proved that it also holds for l≥10.This paper provides a proof of the conjecture for the case of 9≥l≥4.