CN101226687A - Method for analysis of prototype run route in urban traffic - Google Patents
Method for analysis of prototype run route in urban traffic Download PDFInfo
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- CN101226687A CN101226687A CNA2008100595685A CN200810059568A CN101226687A CN 101226687 A CN101226687 A CN 101226687A CN A2008100595685 A CNA2008100595685 A CN A2008100595685A CN 200810059568 A CN200810059568 A CN 200810059568A CN 101226687 A CN101226687 A CN 101226687A
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Abstract
Disclosed is an analytical method for typical running routes in urban traffic, comprising steps as follows: (1) setting a road net topology structure as G = (V, E), vehicle information of every road junction at a corresponding certain time as R = (Ri|i is an element of a set (1,n)), judgment threshold of hotspot junction as k and judgment threshold of typical running route as k', (2) generating first sorting typical running routes between hotspots, which comprises obtaining a hotspot road junction aggregate by filtering road junction volume, in regard to vi is an element of a set V' and Hi is an element of a set H, generating a running route aggregate W' between the hotspots and obtaining a first sorting typical running route W'' by calculating the occupancy of the route according to the generated route W', (3)initially selecting the clustering of the first sorting running route and the generating of the traffic junction merger routes in every clustering aggregate according to the method to obtain the typical running route aggregate W with different particle sizes. The invention is short in processing period, low in cost and high in efficiency, and can reflect the change of the traffic conditions by calculating the typical running route.
Description
Technical field
The present invention relates to urban transportation intellectualizing system field, the method for analysis of prototype run route in especially a kind of urban transportation.
Background technology
The research for the city traffic route at present mainly concentrates on the optimal path that dynamically obtains known starting point, terminal point, and the service object is based on the traffic trip person, lacks the regular information of aspects such as group trip track that vehicle supervision department needs, time.Simultaneously, research and the research of traffic zone of trip track is separated from each other, the path that is obtained is to be the final form of expression with junction node, and lacking consideration is the travel route of unit with the node of different grain size size.
Though have the group trip rule means of obtaining some city road networks at present, mainly contain static OD analytic approach, questionnaire method etc.But have long processing period by the group trip information that these methods are obtained, the high and inefficient problem of cost causes reflecting in time the variation of urban traffic conditions.
Summary of the invention
For the long processing period of obtaining the group trip information, the cost height that overcome existing Traffic Analysis method, efficient is low and can not in time reflect the deficiency that urban traffic conditions changes, the invention provides a kind of processing cycle short, cost is low, efficient is high, by calculating the method for analysis of prototype run route in the urban transportation that prototype run route reflects that in time urban traffic conditions changes.
The technical solution adopted for the present invention to solve the technical problems is:
Method for analysis of prototype run route in a kind of urban transportation may further comprise the steps:
(1), set the road network topology structure be G=(V, E), V={v wherein
i| i ∈ [1, n] } represent each junction node, E={e
Ij| i, j ∈ [1, n-1] }, e
IjThe expression road network in node v
iAnd v
jRelated road markings; The information of vehicles R={R of corresponding a certain each junction node of period
i| i ∈ [1, n] }, the judge threshold value k ' of the judge threshold value k of focus node and prototype run route;
(2), generate the primary election prototype run route between the focus, comprising:
I. obtain focus crossing set V ' by the screening of crossing flow:
A) for
According to v
iVehicle registration H={ (the v of node
i, p
i, t
j) | j ∈ [1, m]), generate set
Wherein
Expression vehicle p
jT in road network
jConstantly appear at junction node v
i
B) generate set
Wherein
Appear at this crossing v first in the expression road network
iThe pairing flow value of vehicle collection;
Ii. for
And
Generate the travel route collection W ' between the focus:
A) will
The vehicle p of middle record
jBe set at current from v
iThe anastomose point that satisfies the need of setting out carries out the vehicle of depth-first traversal and this path of initialization w
i={ v
i);
B) if the junction node v that has access to
k∈ V satisfies condition:
Then with v
kAdd path w
i, be designated as w
i=w
i∪ { v
k), otherwise travel through next node; If the junction node v that has access to
k∈ V ' satisfies condition: v
kBe the focus of not visited among the V ', and
Then stop the road network traversal, w
i=w
i∪ { v
k, W '=W ' ∪ { w
i);
Iii. according to the Route Set W ' that generates, obtain primary election prototype run route W by the occupation rate of calculated route ":
A) set of generation route occupation rate
C (w
i) expression w
iOccurrence number in W ', c (W ' |
Wi) expression and route w
iThe route number that the identical junction node that starts is arranged;
B) the judge threshold value k ' with reference to prototype run route gets ρ '={ ρ (w
i) | ρ (w
i)>k ', w
i∈ W '), the primary election prototype run route collection W "={ w between the focus
i| ρ (w
i)>k ', i ∈ [1, ρ] };
(3), the cluster of primary election prototype run route and the generation of traffic node, comprising:
I. with W " in element as object of classification, set up W " go up the fuzzy resembling relation between each element, and structure fuzzy relation figure R:
A) appoint and get w
i, w
j∈ W ", calculate the similarity statistic between each object of classification
Diff (w
i, w
j) expression route w
i, w
jDifferent junction node number, max (| w
i|, | w
j|) expression w
i, w
jIn long route nodal point number, r
IjCharacterize w
i, w
jBetween similarity degree;
B) calculate W " in similarity statistic r between any two elements
Ij, and with W " in element be node, the similarity statistic r between element
IjBe the limit, constitute fuzzy relation figure R, its matrix representation forms is
Ii. the structure maximum is blured spanning tree TR
MaxInitialization
(n=|W " |), and carry out following processing:
A) get the limit r that has maximum weights among the R
IjCalculate
Be about to r
IjAnd and r
IjThe junction node that the limit is associated adds TR
Max
In R, check TR
MaxEach node and TR
MaxThe weights on outer limit that adjacent node is formed are found out maximal value r wherein
Ij, and calculate
Until TR
MaxIn exist | W " | individual node;
This moment TR
MaxIn node and the limit fuzzy spanning tree of maximum that just constituted R;
By the fuzzy spanning tree TR of maximum
MaxCarry out cluster analysis; Select some λ values to make cut set (λ ∈ [0,1]), with TR
MaxIn disconnect less than the limit of λ, make each continuous node constitute a class, when λ dropped to 0 by 1, the classification of gained was by thin chap, the object of classification of each node representative oneself merger gradually forms a dynamic clustering pedigree chart;
Iii. the route in each cluster set is carried out merger, and generate region junction; To a class
In route analyze, establish such simultaneously and comprise two lines
, w wherein
i={ v
i| i ∈ [m
1, m
2], w
j={ v
j| j ∈ [n
1, n
2]; And definition path w
iVernier be k
1(k
1∈ [m
1, m
2]), w
jVernier be k
2(k
2∈ [n
1, n
2]), the prototype run route after the cluster is stored among the w;
A) with w
iAs the benchmark route, search w
iFirst node v
M1Whether be present in w
jIn, if v
p∈ w
j, s.t.
, then remember w
iVernier k
1=2; w
jVernier k
2=p+1, w=w ∪ { v
j| j ∈ [n
1, k
2-1] }; Otherwise the station location marker amount k of node in the note two-route wire
1=k
2=1;
B) at w
jIn from v
K2Set out and search w
iNode element v
K1+1If exist and it is at w
i, w
jIn subscript be respectively k
1', k
2', then with node set { v
i| i ∈ [k
1, k
1'] ∪ { v
j| j ∈ [k
2, k
2'-1] } as region junction s
K1 ' k2 ', note
, upgrade k simultaneously
1=k
1'+1, k
2=k
2'+1; Otherwise at w
jIn from w
K2Set out and search w
iIn next node;
If k
1>m and k
2<n, then w=w ∪ { v
j| j ∈ [k
2, n] }; If k
1<m and k
2>n, then w=w ∪ { v
i| i ∈ [k
1, m] };
Route in each cluster set is carried out merger by above method obtain to comprise the formed prototype run route collection W of different grain size size.
Technical conceive of the present invention is: adopt the Dynamic OD analytic approach to obtain the typical traffic route of road network, promptly obtain the information of vehicles of each node of road network by methods such as identification equipment, GPS mobile unit or beacon systems, and a certain period in the road network had the road grid traffic node of big flow as the focus of being correlated with, and foundation is the heuristic rule of core with the focus, obtain typical traffic route, simultaneously the route with higher similarity is carried out cluster analysis, finally obtain the formed road network typical case of the node that comprises different grain size size traffic route.
The notion of typical case's traffic route specifically has:
1.1 the literal definition of typical traffic route
Definition: in the oriented road network G of urban transportation, from node S
iTo another one node S
jFormed route t with h node
IjIf all nodes satisfy condition in this route: start from node S
iThe ratio that accounts for by way of this node vehicle of vehicle reach a certain threshold values k, claim that then this route is a h node k type typical case traffic route in this road network.Here S
i, S
jBe the node of certain particle size, the zone that node is made up of several adjacent intersections is single crossing during minimum particle size.
1.2 the mathematical definition of typical traffic route
Definition 1: the topological structure of road network be digraph G=(S, E), S={s wherein
i| i ∈ [1, n] }, E={e
Ij| i, j ∈ [1, n-1] }, s
iThe sign of i node of expression road network comprises one or more contiguous crossings according to the difference of node granularity; e
IjThe expression road network in node s
iAnd s
jRelated road markings.Especially, when the node granularity hour, definition road network G=(V, E), V={v wherein
i| i ∈ [1, n] } represent each junction node, be the special case of S set;
Definition 2: crossing information of vehicles collection H={H
i| i ∈ [1, n] }, H wherein
i={ r
j| j ∈ [1, m] }={ (s
i, p
j, t
j) | j ∈ [1, m] } be illustrated in t
jConstantly by way of crossing s
iVehicle uniqueness information p
jEspecially, when the node granularity hour, H
i={ r
j| j ∈ [1, m] }={ (v
i, p
j, t
j) | j ∈ [1, m] }, v
iRepresent i junction node.
Definition 3: establish route w
i={ s
l| s
l∈ S, l ∈ [0, n] }, the information of vehicles collection of corresponding intersection is R={R
i| i ∈ [1, n] }, the occupation rate of this route then
, c (r wherein
l) represent to start from starting point and arrival crossing s
lVehicle fleet size, c (R
l) represent through crossing s
lVehicle fleet size.
The definition 4: establish road network topology structure G=(S, E), information of vehicles collection H={H
i| i ∈ [1, n] }, then sometime in the territory, typical traffic route collection is W={w among the road network G
i| i ∈ [1, p] }, w wherein
i={ s
l| s
l∈ S, l ∈ [0, n] } be called h node k type typical case traffic route; Satisfy condition: | w
i|=h, θ (w
i)>k.
Prototype run route has following multiple function:
Trip to the public is reasonably induced, and makes things convenient for the public to go on a journey.
Help making rational planning for of public bus network and Public Transport Transfer point, give full play to the transport capacity resource of public transit system, satisfy the needs of public's trip.
Urban transportation information is induced the layout of screen and induced the screen information releasing reasonably to instruct.
The traffic trip amount interregional with road network is research object, obtains its group trip rule.
Beneficial effect of the present invention mainly shows: 1, the processing cycle is short, cost is low, efficient is high, reflects in time that by calculating prototype run route urban traffic conditions changes; 2, can form traffic zone according to the traffic flow situation of current road network, and generate the prototype run route of certain period as unit with different grain size size; 3, not only service to the public of prototype run route, and provide foundation for traffic administration and public bus network, making rational planning for of Public Transport Transfer.The part key road that can choose representative row bus or train route line is provided with the traffic guidance screen, in inducing screen, issue under this road and the transport information of contiguous traffic node, it is for referencial use whether to change travel route for the decision of the group of this route trip vehicle, to improve the validity and the specific aim of the issue of public transport induction information; Public transport company can also this be reference simultaneously, opens relevant public bus network, and sets up the bus station at key event, alleviates the interregional traffic trip pressure of road network trip.
Description of drawings
Fig. 1 is the process flow diagram of prototype run route.
Fig. 2 is the synoptic diagram of experiment road network.
Fig. 3 is the generation synoptic diagram of canonical form route.
Fig. 4 is the demonstration synoptic diagram of region junction.
Embodiment
Below in conjunction with accompanying drawing the present invention is further described.
With reference to Fig. 1~Fig. 4, the method for analysis of prototype run route in a kind of urban transportation, described analytical approach may further comprise the steps:
(1), according to several mathematical definitions of aforementioned typical travel route, setting the road network topology structure is G=(V, E) (definition 1); The information of vehicles R={R of corresponding a certain each junction node of period
i| i ∈ [1, n] } (definition 3), the judge threshold value k ' of the judge threshold value k of focus node and prototype run route.
Focus refers to have the junction node of big flow, and prototype run route often comprises several focuses, obtains prototype run route with the heuristic that is retrieved as of focus, can reduce the blindness of each node of traversal traffic network, improves efficiency of algorithm.
(2), the primary election prototype run route between the generation focus:
At first, find the solution the primary election prototype run route between the focus, algorithm is as follows:
Iii. obtain focus crossing set V ' by the screening of crossing flow;
D) for v
i∈ V is according to v
iThe vehicle registration H of node
i={ (v
i, p
j, t
j) j ∈ [1, m], can generate set
, wherein
Expression vehicle p
j(t first in road network
jConstantly) appear at junction node v
i
E) generate set
, wherein
, appear at this crossing v first in the expression road network
iThe pairing flow value of vehicle collection.
Iv. for v
i∈ V ' reaches
, generate the travel route collection W ' between the focus;
C) will
The vehicle p of middle record
jBe set at current from v
iThe anastomose point that satisfies the need of setting out carries out the vehicle of depth-first traversal and this path of initialization w
i={ v
i.
D) if the junction node v that has access to
k∈ V satisfies condition: (v
k, p
j, t
j) ∈ H
k, then with v
kAdd path w
i, be designated as w
i=w
i∪ { v
k, otherwise travel through next node; If the junction node v that has access to
k∈ V ' satisfies condition: v
kBe the focus of not visited among the V ', and (v
k, p
j, t
j) ∈ H
k, then stop the road network traversal, w
i=w
i∪ { v
k, W '=W ' ∪ { w
i;
Iii. according to the Route Set W ' that generates, obtain primary election prototype run route W " by the occupation rate of calculated route;
C) set of generation route occupation rate
, c (w
i) expression w
iOccurrence number in W ', c (W ' |
Wi) expression and route w
iThe route number that the identical junction node that starts is arranged;
D) the judge threshold value k ' with reference to prototype run route gets ρ '={ ρ (w
i)) | ρ (w
i)>k ', w
i∈ W ' }, the primary election prototype run route collection W "={ w between the focus then
i| ρ (w
i)>k ', i ∈ [1, p] }
(3) generation of the cluster of primary election prototype run route and traffic node:
Primary election prototype run route collection W "; can characterize group travel behaviour to a certain extent between each focus; but obtain route is to be object with the junction node; and the node of coarsegrain often that vehicle supervision department paid close attention in the reality; have certain similarity between the primary election prototype run route that obtains by car tracing between focus simultaneously, be necessary the prototype run route with higher similarity is handled.Here adopt the maximum fuzzy primary election prototype run route W of spanning tree method to obtaining " carry out cluster, finally generate the one group of formed prototype run route collection of the node by different grain size size W, algorithm is as follows:
Iv. with W " in element as object of classification, set up W and " go up the fuzzy resembling relation between each element, and structure fuzzy relation figure R;
A) appoint and get w
i, w
j∈ W ", calculate the similarity statistic between each object of classification
Idff (w
i, w
j) expression route w
i, w
jDifferent junction node number, max (| w
i|, | w
j|) expression w
i, w
jIn long route nodal point number, r
IjCharacterize w
i, w
jBetween similarity degree;
B) calculate W " in similarity statistic r between any two elements
Ij, and with W " in element be node, the similarity statistic r between element
IjBe the limit, constitute fuzzy relation figure R, its matrix representation forms is
V. the structure maximum is blured spanning tree TR
MaxHere initialization
(n=|W " |), and carry out following processing;
B) get the limit r that has maximum weights among the R
IjCalculate
Be about to r
IjAnd and r
IjThe junction node that the limit is associated adds TR
Max
In R, check TR
MaxEach node and TR
MaxThe weights on outer limit that adjacent node is formed are found out maximal value r wherein
Ij, and calculate
Until TR
MaxIn exist | W " | individual node;
This moment TR
MaxIn node and the limit fuzzy spanning tree of maximum that just constituted R;
By the fuzzy spanning tree TR of maximum
MaxCarry out cluster analysis; The concrete practice: select some λ values to make cut set, with TR
MaxIn disconnect less than the limit of λ, make each continuous node constitute a class, when λ dropped to 0 by 1, the classification of gained was by thin chap, the object of classification of each node representative oneself merger gradually forms a dynamic clustering pedigree chart.
Vi. the route in each cluster set is carried out merger, and generate region junction; For for simplicity, only to a class
In route analyze, establish such simultaneously and comprise two lines
, w wherein
i={ v
i| i ∈ [m
1, m
2], w
j={ v
j| j ∈ [n
1, n
2]; And definition path w
iVernier be k
1(k
1∈ [m
1, m
2]), w
jVernier be k
2(k
2∈ [n
1, n
2]), the prototype run route after the cluster is stored among the w;
C) with w
iAs the benchmark route; Search w
iFirst node v
M1Whether be present in w
jIn, if v
p∈ w
j, s.t.
, then remember w
iVernier k
1=2; w
jVernier k
2=p+1, w=w ∪ { v
j| j ∈ [n
1, k
2-1] }; Otherwise the station location marker amount k of node in the note two-route wire
1=k
2=1;
D) at w
jIn from w
K2Set out and search w
iNode element v
K1+1If exist and it is at w
i, w
jIn subscript be respectively k
1', k
2', then with node set { v
i| i ∈ k
1, k
1'] ∪ { v
j| j ∈ [k
2, k
2'-1] } as zone knot s
K1 ' k2 ', note
, upgrade k simultaneously
1=k
1'+1, k
2=k
2'+1; Otherwise at w
jIn from v
K2Set out and search w
iIn next node;
If k
1>m and k
2<n, then w=w ∪ { v
j| j ∈ [k
2, n] }; If k
1<m and k
2>n, then w=w ∪ { v
i| i ∈ [k
1, m] }
Prototype run route in the road network can obtain to comprise the formed prototype run route collection W of different grain size size by the route in each cluster set is carried out merger by above method.
Be that example is analyzed now with city of Hangzhou piece traffic network, (major trunk roads identify with black) as shown in Figure 2, this network is made up of 25 junction node and 45 sections turnpike roads.
The candid photograph information of vehicles that system was obtained according to each crossing of this road network in one day, pass judgment on k=30000/day of threshold value in conjunction with the focus node that the selected aforementioned part of historical data and expertise value is mentioned, and prototype run route is passed judgment on threshold value k '=0.7, and analyze according to the algorithm of this part introduction, the prototype run route result who obtains is as shown in Figure 3.
Among Fig. 3, wherein the part with underscore is the region junction that comprises relevant crossing, and represents this region junction with the crossing of vehicle flowrate maximum in this zone, as shown in Figure 4, but clicks the crossing that this node viewing area is comprised.
Fig. 3, prototype run route dynamic reflection shown in Figure 4 group trip route in the road network, the part key road that vehicle supervision department can choose prototype run route is provided with the traffic guidance screen, in inducing screen, issue under this road and the transport information of contiguous traffic node, going out to travel for the group of this route, whether to change travel route for referencial use in a decision, to improve the validity and the specific aim of the issue of public transport induction information; Public transport company can also this be reference simultaneously, opens relevant public bus network, and sets up the bus station at key event, alleviates the interregional traffic trip pressure of road network trip.
Claims (1)
1. the method for analysis of prototype run route in the urban transportation, it is characterized in that: described analytical approach may further comprise the steps:
(1), set the road network topology structure be G=(V, E), V={v wherein
i| i ∈ [1, n] } represent each junction node,
E={e
Ij| i, j ∈ [1, n-1] }, e
IjThe expression road network in node v
iAnd v
jRelated road markings; The information of vehicles R={R of corresponding a certain each junction node of period
i| i ∈ [1, n] }, the judge threshold value k ' of the judge threshold value k of focus node and prototype run route;
(2), generate the primary election prototype run route between the focus, comprising:
I. obtain focus crossing set V ' by the screening of crossing flow:
A) for v
i∈ V is according to v
iThe vehicle registration H of node
i={ (v
i, p
j, t
j) | [1, m} generates set to j ∈
Wherein
Expression vehicle p
jT in road network
jConstantly appear at junction node v
i
B) generate set
Wherein
Appear at this crossing v first in the expression road network
iThe pairing flow value of vehicle collection;
Ii. for v
i∈ V ' reaches
, generate the travel route collection W ' between the focus:
A) will
The vehicle p of middle record
jBe set at current from v
iThe anastomose point that satisfies the need of setting out carries out the vehicle of depth-first traversal and this path of initialization w
i={ v
i;
B) if the junction node v that has access to
k∈ V satisfies condition: (v
k, p
j, t
j) ∈ H
k, then with v
kAdd path w
i, be designated as w
i=w
i∪ { v
k, otherwise travel through next node; If the junction node v that has access to
k∈ V ' satisfies condition: v
kBe the focus of not visited among the V ', and (v
k, p
j, t
j) ∈ H
k, then stop the road network traversal, w
i=w
i∪ { v
k, W '=W ' ∪ { w
i;
Iii. according to the Route Set W ' that generates, obtain primary election prototype run route W by the occupation rate of calculated route ":
A) set of generation route occupation rate
w
i∈ W ' }, c (w
i) expression w
iOccurrence number in W ', c (W ' |
Wi) expression and route w
iThe route number that the identical junction node that starts is arranged;
B) the judge threshold value k ' with reference to prototype run route gets ρ '={ ρ (w
i) | ρ (w
i)>k ', w
i∈ W ' }, the primary election prototype run route collection W "={ w between the focus
i| ρ (w
i)>k ', i ∈ [1, p] };
(3), the cluster of primary election prototype run route and the generation of traffic node, comprising:
I. with W " in element as object of classification, set up W " go up the fuzzy resembling relation between each element, and structure fuzzy relation figure R:
A) appoint and get w
i, w
j∈ W ", calculate the similarity statistic between each object of classification
Diff (w
i, w
j) expression route w
i, w
jDifferent junction node number, max (| w
i|, | w
j|) expression w
i, w
jIn long route nodal point number, r
IjCharacterize w
i, w
jBetween similarity degree;
B) calculate W " in similarity statistic r between any two elements
Ij, and with W " in element be node, the similarity statistic r between element
IjBe the limit, constitute fuzzy relation figure R, its matrix representation forms is
Ii. the structure maximum is blured spanning tree TR
MaxInitialization
(n=|W " |), and carry out following processing:
A) get the limit r that has maximum weights among the R
IjCalculate
Be about to r
IjAnd and r
IjThe junction node that the limit is associated adds TR
Max
In R, check TR
MaxEach node and TR
MaxThe weights on outer limit that adjacent node is formed are found out maximal value r wherein
Ij', and calculate
Until TR
MaxIn exist | W " | individual node;
This moment TR
MaxIn node and the limit fuzzy spanning tree of maximum that just constituted R;
By the fuzzy spanning tree TR of maximum
MaxCarry out cluster analysis; Select some λ values to make cut set (λ ∈ [0,1]), with TR
MaxIn disconnect less than the limit of λ, make each continuous node constitute a class, when λ dropped to 0 by 1, the classification of gained was by thin chap, the object of classification of each node representative oneself merger gradually forms a dynamic clustering pedigree chart;
Iii. the route in each cluster set is carried out merger, and generate region junction; To a class
In route analyze, establish such simultaneously and comprise two lines
, w wherein
i={ v
i| i ∈ [m
1, m
2], w
j={ v
j| j ∈ [n
1, n
2]; And definition path w
iVernier be k
1(k
1∈ [m
1, m
2]), w
jVernier be k
2(k
2∈ [n
1, n
2]), the prototype run route after the cluster is stored among the w;
A) with w
iAs the benchmark route, search w
iFirst node v
M1Whether be present in w
jIn, if v
p∈ w
j, s.t.v
p=v
M1, then remember w
iVernier k
1=2; w
jVernier k
2=p+1, w=w ∪ { v
j| j ∈ [n
1, k
2-1] }; Otherwise the station location marker amount k of node in the note two-route wire
1=k
2=1;
B) at w
jIn from v
K2Set out and search w
iNode element v
K1+1If exist and it is at w
i, w
jIn subscript be respectively k
1', k
2', then with node set { v
i| i ∈ [k
1, k
1' ∪ { v
j| j ∈ [k
2, k
2'-1] } as region junction s
K1 ' k2 ', note
, upgrade k simultaneously
1=k
1'+1, k
2=k
2'+1; Otherwise at w
jIn from v
K2Set out and search w
iIn next node;
If k
1>m and k
2<n, then w=w ∪ { v
j| j ∈ [k
2, n] }; If k
1<m and k
2>n, then w=w ∪ { v
i| i ∈ [k
1, m] }.
Route in each cluster set is carried out merger by above method obtain to comprise the formed prototype run route collection W of different grain size size.
Priority Applications (1)
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