Background Atrial tachycardia(AT)with cycle length(CL)alternans is uncommon and conventional mapping of this AT remains challenging. We used an ultrahigh density mapping system to rapidly map complicated circuits with...Background Atrial tachycardia(AT)with cycle length(CL)alternans is uncommon and conventional mapping of this AT remains challenging. We used an ultrahigh density mapping system to rapidly map complicated circuits with sufficient spatial resolution and electrogram quality to elucidate the precise mechanism of this special ATs. Methods Of 210 consecutive patients with clinical ATs who underwent catheter ablation with the ultrahigh density mapping system,4 patients(1.9%)with CL alternans were identified. The AT alternating cycles mapped by the Rhythmia mapping system for long CL were 317±51(range 245-355)ms and for short CL were 282±51(range 235-333)ms. Both long and short cycles followed in 1∶1 sequence in all 4 patients(longshort-long-short). Results By comparing the separate maps with long and short CL,we classified ATs with CL alternans into 2 types. In type 1,CL alternans resulted from an intermittent 2∶1 conduction block through the slow conduction channel in the small circuit. In type 2,CL alternans caused by the alternated conduction velocity passing through the conduction gap were manifested. Ablation at the fractionated potentials contributes to the termination of AT in 3 of the 4 patients. Conclusions Ultrahigh density mapping system can accurately identify the mechanism of complex ATs with alternating CL. The CL alternans may be related to the intermittent conduction block within the channel of the small circuitor different conduction velocity through the identical channel. Fractionated electrogram recorded in the common isthmus or some"conduction gaps"may be a reasonable approach to terminate these ATs.展开更多
The cycle length distribution of a graph of order n is denoted by (c1,c2,...,cn), where ci is the number of cycles of length i. In this paper, we obtain that a graph G is uniquely determined by its cycle distribution ...The cycle length distribution of a graph of order n is denoted by (c1,c2,...,cn), where ci is the number of cycles of length i. In this paper, we obtain that a graph G is uniquely determined by its cycle distribution if: (1) G = Kn,n+7 (n ≥ 10); or (2) G = Kn,n+7 - A (|A| = 1,n ≥ 12); or (3) G = Kn,n+7 - A (|A| = 2,n ≥ 14); or (4) G = Kn,n+7 - (|A| = 3,n ≥ 16), where A - E(Kn,n+7).展开更多
The cycle length distribution of a graph G of order n is a sequence （c1 （G）,…, cn （G））, where ci （G） is the number of cycles of length i in G. In general, the graphs with cycle length distribution （c1（G） ,...The cycle length distribution of a graph G of order n is a sequence （c1 （G）,…, cn （G））, where ci （G） is the number of cycles of length i in G. In general, the graphs with cycle length distribution （c1（G） ,…,cn（G）） are not unique. A graph G is determined by its cycle length distribution if the graph with cycle length distribution （c1 （G）,…, cn （G）） is unique. Let Kn,n＋r be a complete bipartite graph and A lohtaib in E（Kn,n＋r）. In this paper, we obtain： Let s 〉 1 be an integer. （1） If r = 2s, n 〉 s（s - 1） ＋ 2｜A｜, then Kn,n＋r - A （A lohtain in E（Kn,n＋r）,｜A｜ ≤ 3） is determined by its cycle length distribution; （2） If r = 2s ＋ 1,n 〉 s^2 ＋ 2｜A｜, Kn,n＋r - A （A lohtain in E（Kn,n＋r）, ｜A｜ ≤3） is determined by its cycle length distribution.展开更多
Characterization of sign patterns that allow diagonalizability has been a long-standing open problem.In this paper,we obtain some sufficient and/or necessary conditions for a sign pattern to allow diagonalizability.Mo...Characterization of sign patterns that allow diagonalizability has been a long-standing open problem.In this paper,we obtain some sufficient and/or necessary conditions for a sign pattern to allow diagonalizability.Moreover,we determine how many entries need to be changed to obtain a matrix B′∈Q(A)with rank MR(A)from a matrix B∈Q(A)with rank mr(A).Finally,we also obtain some results on a sign pattern matrix in Frobenius normal form that allows diagonalizability.展开更多
As known to all that Henon chaotic system is not appropriate for generating the key-streams because it has non-uniformly distributed output signal, a new key-stream generation scheme based on Henon chaotic system is p...As known to all that Henon chaotic system is not appropriate for generating the key-streams because it has non-uniformly distributed output signal, a new key-stream generation scheme based on Henon chaotic system is presented. In order to get the key-streams with good statistics and long enough cycle length, a specific method for dividing the enon attractor into numerous non-overlapping sub-regions, and a new one-to-one mapping strategy between the divided sub-regions and elements of dynamically generated matrix consisting of O＇s and l＇s are proposed. Experimental results demonstrate that the generated key-streams are with long enough cycle length and very sensitive to the initial values and secret keys. For example, key-streams with the cycle length of 10^32 can easily be obtained. Moreover, even if the fluctuation to the initial values or secret keys is as small as 10^- 14 uncorrelated key-streams will be generated. Experimental results also demonstrate that the generated key-streams have good randomness and they can pass all the standard criteria specified in FIPS PUB 140^-2 with no less than 98%.展开更多
Rendezvous is a blind process establishing a communication link on a common channel between a pair of nodes in cognitive radio networks. We propose two guaranteed rendezvous algorithms for cognitive radio networks und...Rendezvous is a blind process establishing a communication link on a common channel between a pair of nodes in cognitive radio networks. We propose two guaranteed rendezvous algorithms for cognitive radio networks under both single-radio and multi-radio scenarios with an asynchronous setting. For single-radio scenario, each cycle length is a prime number associated with a channel hopping sequence.The rendezvous can be guaranteed as long as the IDs of the two nodes are different. For multi-radio scenario, we propose a cycle length and rotation based rendezvous algorithm. Each node generates a channel hopping sequence with only one cycle length. Then these radios of each nodes rotate on the generated sequence with different rotation numbers at each hopping cycle. The rendezvous between two nodes is guaranteed as long as they have different cycle lengths or the same cycle length with different number of rotations. We conduct simulations on three metrics and the results show that the proposed algorithms outperform the existing ones.展开更多
Existing optimization methodologies for intersection operations assumes a fixed geometric design, however the geometry and operational system should be simultaneously optimized to produce the best performance. Signali...Existing optimization methodologies for intersection operations assumes a fixed geometric design, however the geometry and operational system should be simultaneously optimized to produce the best performance. Signalized crosswalks are complex and critical pedestrian facilities. Their geometry and configuration directly affect the safety, cycle length and resulting delays for all users. As crosswalks become wider or they are placed further upstream, the cycle length will increase due to the all-red time requirement, which deteriorates the overall mobility levels of signalized intersections. In contrast, when crosswalk width decreases, the required minimum pedestrian crossing time increases due to the bi-directional pedestrian flow effects, which leads to longer cycle length. Furthermore, existing manuals and guidelines do not offer any specification for the required crosswalk width under various pedestrian demand conditions. This study aims to propose new criteria for designing crosswalk width at signalized intersections, which can optimize the performance from the viewpoint of vehicular traffic and pedestrians. The proposed methodology considers pedestrian demand and its characteristics （such as bi-directional flow effects）, vehicle demand and the geometric characteristics of the intersection The concept of optimized crosswalk width is proposed and demonstrated through a case study. Moreover, a comprehensive discussion regarding the merits and drawbacks of existing strategies on positioning crosswalks is presented. It was found that at signalized intersections, which are characterized by low pedestrian and high vehicle demands, crosswalk width of 2 meters is appropriate to minimize cycle length and resulting delays for all users including pedestrians.展开更多
The relationship between the length of the solar cycle, a good indicator of long-term change in solar activity, and natural disasters (drought, flood, and strong earthquakes) in China during the last 108 yearsis analy...The relationship between the length of the solar cycle, a good indicator of long-term change in solar activity, and natural disasters (drought, flood, and strong earthquakes) in China during the last 108 yearsis analyzed. The results suggest that the length of solar cycle may be a useful indicator for drought/flood and strong earthquakes. When the solar activity strengthens, we see the length of the solar cycle shorten and more floods occur in South China and frequent strong earthquakes happen in the Tibetan Plateau, but the droughts in East China as well as the strong earthquakes in Taiwan and at the western boundary of China are very few. The opposite frequencies occur when the solar activity weakens. The current study indicates that the solar activity may play an important role in the climate extremes and behavior in the lithosphere.展开更多
Shelf-basin advection is essential to subsistence of the Arctic copepod Calanus hyperboreus population in high basin area. Its abundance, population structure and body size in pelagic layer were investigated with samp...Shelf-basin advection is essential to subsistence of the Arctic copepod Calanus hyperboreus population in high basin area. Its abundance, population structure and body size in pelagic layer were investigated with samples collected over a large range in the western Arctic Ocean during summer 2003, to evaluate the geographical variation in recruitment pattern. Calanus hyperboreus was absent from the shallow areas of the Chukchi Sea and most abundant in the slope area between the Chukchi Sea and Chukchi Abyssal Plain（CS-slope）. Total abundance varied between 1 110.0 and 5 815.0 ind./m^2 in the CS-slope area and ranged from 40.0 to 950.0 ind./m^2 in the other areas. Early stages（CI–IV） dominated in the CS-slope area, whereas CV and adult females were frequently recorded only in deep basin areas. Geographical difference of prosome length was most evident in CIII,with average ranging from 2.48 to 2.61 mm at the CS-slope stations and 2.16–2.37 mm at the others. Abundance of early developmental stages（CI–CIV） correlated positively with Chl a concentration, but negative correlation was observed in late stages（CV–adult）. Our results indicated that C. hyperboreus can benefit from primary production increase through accelerated development in the first growth season and the productive CS-slope area is a potential source for slope-basin replenishment.展开更多
This article deals with the behavior of two-dimensional(2-D)cellular automata(CA)with a special rule under periodic boundary condition by using matrix algebra.The important characteristics of CA have been studied,such...This article deals with the behavior of two-dimensional(2-D)cellular automata(CA)with a special rule under periodic boundary condition by using matrix algebra.The important characteristics of CA have been studied,such as Garden of Eden(GOE),maximal transient length,maximal cycle length and so forth.Several necessary and sufficient conditions are provided,which guarantee a given configuration of being a GOE in different cases.Besides,algorithms are proposed to obtain the number of GOEs,the maximal transient length,and the maximal cycle length in such a CA with the rule mentioned above under periodic condition.展开更多
This paper considers sales mode selection issues for a two-echelon supply chain of perishable products involving a supplier and a retailer.Consumers’purchase desire is assumed to be positive correlation with the fres...This paper considers sales mode selection issues for a two-echelon supply chain of perishable products involving a supplier and a retailer.Consumers’purchase desire is assumed to be positive correlation with the freshness of the product.First,the traditional sales mode is examined,in which the supplier and the retailer play a Stackelberg game.We propose a three-layer decision model for this situation,and obtain dynamic pricing strategies and selling cycle length.It is shown that the retailer has little motivation to order many perishable products so as to avoid a long selling cycle length.Second,the commission-charge mode is analyzed,in which the retailer declares its decision first.In this mode,we demonstrate that the perishable product will be on sale during the whole shelf life under a certain condition.The correlation between the sales price of each stage and the remaining shelf-life length is analyzed.Third,the superiority analysis for the two sales modes is conducted.We show the relation between the selling cycle lengths of the two modes.By our analysis,it is shown that both the supplier and the retailer gain more profits when the commission-charge mode is adopted and the commission rate locates in a certain open interval.Finally,a numerical illustration is presented to visualize the discussed models,and some supplements are made for the acquired conclusions by the illustration.展开更多
Let G be a simple graph. A total coloring f of G is called E-total-coloring if no two adjacent vertices of G receive the same color and no edge of G receives the same color as one of its endpoints. For E-total-colorin...Let G be a simple graph. A total coloring f of G is called E-total-coloring if no two adjacent vertices of G receive the same color and no edge of G receives the same color as one of its endpoints. For E-total-coloring f of a graph G and any vertex u of G, let Cf （u） or C（u） denote the set of colors of vertex u and the edges incident to u. We call C（u） the color set of u. If C（u） ≠ C（v） for any two different vertices u and v of V（G）, then we say that f is a vertex-distinguishing E-total-coloring of G, or a VDET coloring of G for short. The minimum number of colors required for a VDET colorings of G is denoted by X^evt（G）, and it is called the VDET chromatic number of G. In this article, we will discuss vertex-distinguishing E-total colorings of the graphs mC3 and mC4.展开更多
In this paper,a sequential algorithm computing the all vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is sho...In this paper,a sequential algorithm computing the all vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is shown.This method can also be used to get a parallel algorithm to compute transitive closure arrayof an undirected graph.The time complexify of the parallel algorithm is O(n^3/p).If D,P andare known,it is shown that the problems to find all connected components, to compute the diameter of an undirected graph,to determine the center of a directed graph and to search for a directed cycle with the minimum(maximum)length in a directed graph can all be solved in O(n^2/p^+ logp)time.展开更多
基金supported by the Key Research and Development Projects of Guangdong Province(No. 2019B020230004)the National Key Research and Development Projects (No. 2018YFC1312501/2018YFC1312502)the National Natural Science Foundation (No. 81870254)
文摘Background Atrial tachycardia(AT)with cycle length(CL)alternans is uncommon and conventional mapping of this AT remains challenging. We used an ultrahigh density mapping system to rapidly map complicated circuits with sufficient spatial resolution and electrogram quality to elucidate the precise mechanism of this special ATs. Methods Of 210 consecutive patients with clinical ATs who underwent catheter ablation with the ultrahigh density mapping system,4 patients(1.9%)with CL alternans were identified. The AT alternating cycles mapped by the Rhythmia mapping system for long CL were 317±51(range 245-355)ms and for short CL were 282±51(range 235-333)ms. Both long and short cycles followed in 1∶1 sequence in all 4 patients(longshort-long-short). Results By comparing the separate maps with long and short CL,we classified ATs with CL alternans into 2 types. In type 1,CL alternans resulted from an intermittent 2∶1 conduction block through the slow conduction channel in the small circuit. In type 2,CL alternans caused by the alternated conduction velocity passing through the conduction gap were manifested. Ablation at the fractionated potentials contributes to the termination of AT in 3 of the 4 patients. Conclusions Ultrahigh density mapping system can accurately identify the mechanism of complex ATs with alternating CL. The CL alternans may be related to the intermittent conduction block within the channel of the small circuitor different conduction velocity through the identical channel. Fractionated electrogram recorded in the common isthmus or some"conduction gaps"may be a reasonable approach to terminate these ATs.
基金the Science Foundation of Shanghai Municipal Education Commission (No.04DB25)
文摘The cycle length distribution of a graph of order n is denoted by (c1,c2,...,cn), where ci is the number of cycles of length i. In this paper, we obtain that a graph G is uniquely determined by its cycle distribution if: (1) G = Kn,n+7 (n ≥ 10); or (2) G = Kn,n+7 - A (|A| = 1,n ≥ 12); or (3) G = Kn,n+7 - A (|A| = 2,n ≥ 14); or (4) G = Kn,n+7 - (|A| = 3,n ≥ 16), where A - E(Kn,n+7).
基金the National Natural Science Foundation of China(Nos.1070106810671191)
文摘The cycle length distribution of a graph G of order n is a sequence （c1 （G）,…, cn （G））, where ci （G） is the number of cycles of length i in G. In general, the graphs with cycle length distribution （c1（G） ,…,cn（G）） are not unique. A graph G is determined by its cycle length distribution if the graph with cycle length distribution （c1 （G）,…, cn （G）） is unique. Let Kn,n＋r be a complete bipartite graph and A lohtaib in E（Kn,n＋r）. In this paper, we obtain： Let s 〉 1 be an integer. （1） If r = 2s, n 〉 s（s - 1） ＋ 2｜A｜, then Kn,n＋r - A （A lohtain in E（Kn,n＋r）,｜A｜ ≤ 3） is determined by its cycle length distribution; （2） If r = 2s ＋ 1,n 〉 s^2 ＋ 2｜A｜, Kn,n＋r - A （A lohtain in E（Kn,n＋r）, ｜A｜ ≤3） is determined by its cycle length distribution.
基金Supported by Research Project of Leshan Normal University(Grant No.LZD016)。
文摘Characterization of sign patterns that allow diagonalizability has been a long-standing open problem.In this paper,we obtain some sufficient and/or necessary conditions for a sign pattern to allow diagonalizability.Moreover,we determine how many entries need to be changed to obtain a matrix B′∈Q(A)with rank MR(A)from a matrix B∈Q(A)with rank mr(A).Finally,we also obtain some results on a sign pattern matrix in Frobenius normal form that allows diagonalizability.
基金Foundation item： Proj ects（61172184, 61173147） supported by the National Natural Science Foundation of China Project（12JJ6062） supported by Natural Science Foundation of Hunan Province, China+1 种基金 Project（121gpy31） supported by the Fundamental Research Funds for the Central Universities of China Project supported by the State Key Laboratory of Information Security （Institute of Software, Chinese Academy of Sciences）, China
文摘As known to all that Henon chaotic system is not appropriate for generating the key-streams because it has non-uniformly distributed output signal, a new key-stream generation scheme based on Henon chaotic system is presented. In order to get the key-streams with good statistics and long enough cycle length, a specific method for dividing the enon attractor into numerous non-overlapping sub-regions, and a new one-to-one mapping strategy between the divided sub-regions and elements of dynamically generated matrix consisting of O＇s and l＇s are proposed. Experimental results demonstrate that the generated key-streams are with long enough cycle length and very sensitive to the initial values and secret keys. For example, key-streams with the cycle length of 10^32 can easily be obtained. Moreover, even if the fluctuation to the initial values or secret keys is as small as 10^- 14 uncorrelated key-streams will be generated. Experimental results also demonstrate that the generated key-streams have good randomness and they can pass all the standard criteria specified in FIPS PUB 140^-2 with no less than 98%.
基金supported in part by NSF under the grant CNS-1526152
文摘Rendezvous is a blind process establishing a communication link on a common channel between a pair of nodes in cognitive radio networks. We propose two guaranteed rendezvous algorithms for cognitive radio networks under both single-radio and multi-radio scenarios with an asynchronous setting. For single-radio scenario, each cycle length is a prime number associated with a channel hopping sequence.The rendezvous can be guaranteed as long as the IDs of the two nodes are different. For multi-radio scenario, we propose a cycle length and rotation based rendezvous algorithm. Each node generates a channel hopping sequence with only one cycle length. Then these radios of each nodes rotate on the generated sequence with different rotation numbers at each hopping cycle. The rendezvous between two nodes is guaranteed as long as they have different cycle lengths or the same cycle length with different number of rotations. We conduct simulations on three metrics and the results show that the proposed algorithms outperform the existing ones.
文摘Existing optimization methodologies for intersection operations assumes a fixed geometric design, however the geometry and operational system should be simultaneously optimized to produce the best performance. Signalized crosswalks are complex and critical pedestrian facilities. Their geometry and configuration directly affect the safety, cycle length and resulting delays for all users. As crosswalks become wider or they are placed further upstream, the cycle length will increase due to the all-red time requirement, which deteriorates the overall mobility levels of signalized intersections. In contrast, when crosswalk width decreases, the required minimum pedestrian crossing time increases due to the bi-directional pedestrian flow effects, which leads to longer cycle length. Furthermore, existing manuals and guidelines do not offer any specification for the required crosswalk width under various pedestrian demand conditions. This study aims to propose new criteria for designing crosswalk width at signalized intersections, which can optimize the performance from the viewpoint of vehicular traffic and pedestrians. The proposed methodology considers pedestrian demand and its characteristics （such as bi-directional flow effects）, vehicle demand and the geometric characteristics of the intersection The concept of optimized crosswalk width is proposed and demonstrated through a case study. Moreover, a comprehensive discussion regarding the merits and drawbacks of existing strategies on positioning crosswalks is presented. It was found that at signalized intersections, which are characterized by low pedestrian and high vehicle demands, crosswalk width of 2 meters is appropriate to minimize cycle length and resulting delays for all users including pedestrians.
基金supported by the China National Key Programme for Developing Basic Sciences(G1998040800)
文摘The relationship between the length of the solar cycle, a good indicator of long-term change in solar activity, and natural disasters (drought, flood, and strong earthquakes) in China during the last 108 yearsis analyzed. The results suggest that the length of solar cycle may be a useful indicator for drought/flood and strong earthquakes. When the solar activity strengthens, we see the length of the solar cycle shorten and more floods occur in South China and frequent strong earthquakes happen in the Tibetan Plateau, but the droughts in East China as well as the strong earthquakes in Taiwan and at the western boundary of China are very few. The opposite frequencies occur when the solar activity weakens. The current study indicates that the solar activity may play an important role in the climate extremes and behavior in the lithosphere.
基金The National Natural Science Foundation of China under contract No.40406002the Public Science and Technology Research Funds Projects of Ocean under contract No.201105022
文摘Shelf-basin advection is essential to subsistence of the Arctic copepod Calanus hyperboreus population in high basin area. Its abundance, population structure and body size in pelagic layer were investigated with samples collected over a large range in the western Arctic Ocean during summer 2003, to evaluate the geographical variation in recruitment pattern. Calanus hyperboreus was absent from the shallow areas of the Chukchi Sea and most abundant in the slope area between the Chukchi Sea and Chukchi Abyssal Plain（CS-slope）. Total abundance varied between 1 110.0 and 5 815.0 ind./m^2 in the CS-slope area and ranged from 40.0 to 950.0 ind./m^2 in the other areas. Early stages（CI–IV） dominated in the CS-slope area, whereas CV and adult females were frequently recorded only in deep basin areas. Geographical difference of prosome length was most evident in CIII,with average ranging from 2.48 to 2.61 mm at the CS-slope stations and 2.16–2.37 mm at the others. Abundance of early developmental stages（CI–CIV） correlated positively with Chl a concentration, but negative correlation was observed in late stages（CV–adult）. Our results indicated that C. hyperboreus can benefit from primary production increase through accelerated development in the first growth season and the productive CS-slope area is a potential source for slope-basin replenishment.
基金supported by the National Natural Science Foundation of China(60473005)the Guangxi Natural Science Foundation(0640061,0832103)
文摘This article deals with the behavior of two-dimensional(2-D)cellular automata(CA)with a special rule under periodic boundary condition by using matrix algebra.The important characteristics of CA have been studied,such as Garden of Eden(GOE),maximal transient length,maximal cycle length and so forth.Several necessary and sufficient conditions are provided,which guarantee a given configuration of being a GOE in different cases.Besides,algorithms are proposed to obtain the number of GOEs,the maximal transient length,and the maximal cycle length in such a CA with the rule mentioned above under periodic condition.
文摘This paper considers sales mode selection issues for a two-echelon supply chain of perishable products involving a supplier and a retailer.Consumers’purchase desire is assumed to be positive correlation with the freshness of the product.First,the traditional sales mode is examined,in which the supplier and the retailer play a Stackelberg game.We propose a three-layer decision model for this situation,and obtain dynamic pricing strategies and selling cycle length.It is shown that the retailer has little motivation to order many perishable products so as to avoid a long selling cycle length.Second,the commission-charge mode is analyzed,in which the retailer declares its decision first.In this mode,we demonstrate that the perishable product will be on sale during the whole shelf life under a certain condition.The correlation between the sales price of each stage and the remaining shelf-life length is analyzed.Third,the superiority analysis for the two sales modes is conducted.We show the relation between the selling cycle lengths of the two modes.By our analysis,it is shown that both the supplier and the retailer gain more profits when the commission-charge mode is adopted and the commission rate locates in a certain open interval.Finally,a numerical illustration is presented to visualize the discussed models,and some supplements are made for the acquired conclusions by the illustration.
基金Supported by the National Natural Science Foundation of China (Grant No.10771091)the Scientific Research Project of Northwest Normal University (Grant No.NWNU-KJCXGC-03-61)
文摘Let G be a simple graph. A total coloring f of G is called E-total-coloring if no two adjacent vertices of G receive the same color and no edge of G receives the same color as one of its endpoints. For E-total-coloring f of a graph G and any vertex u of G, let Cf （u） or C（u） denote the set of colors of vertex u and the edges incident to u. We call C（u） the color set of u. If C（u） ≠ C（v） for any two different vertices u and v of V（G）, then we say that f is a vertex-distinguishing E-total-coloring of G, or a VDET coloring of G for short. The minimum number of colors required for a VDET colorings of G is denoted by X^evt（G）, and it is called the VDET chromatic number of G. In this article, we will discuss vertex-distinguishing E-total colorings of the graphs mC3 and mC4.
基金Research supported by the Science Foundation of Shandong Province.
文摘In this paper,a sequential algorithm computing the all vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is shown.This method can also be used to get a parallel algorithm to compute transitive closure arrayof an undirected graph.The time complexify of the parallel algorithm is O(n^3/p).If D,P andare known,it is shown that the problems to find all connected components, to compute the diameter of an undirected graph,to determine the center of a directed graph and to search for a directed cycle with the minimum(maximum)length in a directed graph can all be solved in O(n^2/p^+ logp)time.
