WO2007061264A1 - Reducing method of shortest path searching area and calculating method of minimal expecting load and method of searching shortest path - Google Patents

Reducing method of shortest path searching area and calculating method of minimal expecting load and method of searching shortest path Download PDF

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WO2007061264A1
WO2007061264A1 PCT/KR2006/005003 KR2006005003W WO2007061264A1 WO 2007061264 A1 WO2007061264 A1 WO 2007061264A1 KR 2006005003 W KR2006005003 W KR 2006005003W WO 2007061264 A1 WO2007061264 A1 WO 2007061264A1
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node
step
distance
search
cost
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PCT/KR2006/005003
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French (fr)
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Yeong-Geun Ryu
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Yeong-Geun Ryu
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in preceding groups
    • G01C21/26Navigation; Navigational instruments not provided for in preceding groups specially adapted for navigation in a road network
    • G01C21/34Route searching; Route guidance
    • G01C21/3453Special cost functions, i.e. other than distance or default speed limit of road segments
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in preceding groups
    • G01C21/26Navigation; Navigational instruments not provided for in preceding groups specially adapted for navigation in a road network
    • G01C21/34Route searching; Route guidance
    • G01C21/3446Details of route searching algorithms, e.g. Dijkstra, A*, arc-flags, using precalculated routes

Abstract

The present invention relates to a method of limiting a search area for searching for a shortest path on a complex network in a further speedy way, and a method of calculating a minimum expected cost and a method of searching for a shortest distance using the same. More specifically, the present invention relates to a method of reducing a search area using a minimum basic unit of spatial-distance-based true cost and searching for the shortest path within the reduced search area again using the minimum basic unit of spatial-distance -based true cost.

Description

Description

REDUCEING METHOD OF SHORTEST PATH SEARCHING AREA AND CALCULATING METHOD OF MINIMAL EXPECTING LOAD AND METHOD OF SEARCHING

SHORTEST PATH Technical Field

[1] The present invention relates to a method of limiting a search area for searching for a shortest path on a complex network in a further speedy way, and a method of calculating a minimum expected cost and a method of searching for a shortest distance using the same. More specifically, the present invention relates to a method of reducing a search area using a minimum basic unit of spatial-distance-based true cost and searching for a shortest path within the reduced search area again using the minimum basic unit of spatial-distance-based true cost. Background Art

[2] The methods of searching for a shortest path are used in a variety of fields, such as car navigation system, communication networks, game software, artificial intelligence, or the like. Representative algorithms among the search algorithms known up to date include the Dijkstra's algorithm, Floyd algorithm, A* algorithm, and the like.

[3] The Dijkstra's algorithm is a method of selecting by comparison a path having a minimum time distance among directly connected paths starting from a starting node regardless of directionality toward a destination node. However, it has a problem in that searching time is considerably extended in a network of a quite large scale.

[4] The Floyd algorithm also examines and compares all possible links from a starting node to a destination node to find a shortest path, and thus has a problem in that searching time is considerably prolonged as is the same with the Dijkstra's algorithm.

[5] The A* algorithm is a representative of heuristic algorithms, which deduces a shortest path using a minimum cost estimator of residual paths from a current node to a destination node. That is, the algorithm searches for a shortest path using real distance from a starting node to the current node and estimated distance from the current node to the destination node (generally, a straight-line distance), and thus has directionality. Therefore, the A* algorithm is advantageous over the Dijkstra's algorithm or the Floyd algorithm in that searching time is reduced. However, it is disadvantageous in that the minimum cost estimator of residual paths cannot be easily determined, and further, if the minimum cost estimate is mistakenly selected, it may not get a solution. Furthermore, if a straight distance is simply adopted as an estimator, searching can be ineffective depending on the structure of a network.

[6] In addition, existing searching methods are inefficiently performed in that after a search is completed, a shortest path is provided through performing an inverse search (restoration) function from the destination node to the starting node using connection relations between nodes. Disclosure of Invention Technical Problem

[7] Accordingly, the present invention has been made in order to solve the above problems, and it is an object of the present invention to provide a method of searching for a shortest path from a starting node to a destination node in a correct and speedy way in any network configuration, the method comprising the steps of constructing a temporary shortest path having directly connected nodes while minimizing the sum of spatial distances between the starting node and the destination node, obtaining a minimum basic unit of spatial-distance-based true cost by dividing a true cost, such as expense, time, real distance, or the like, by a spatial distance, reducing a search area to a range having a spatial distance that is smaller than a value of the true cost of the temporary shortest path divided by the minimum basic unit of spatial-distance-based true cost, and calculating a minimum expected cost using the minimum basic unit of spatial-distance-based true cost and spatial distances within the reduced search range, without searching for entire nodes by comparing the minimum expected cost with the true cost of the temporary shortest path.

Technical Solution

[8] In order to accomplish the above object of the invention, according to one aspect of the invention, there is provided a method of reducing a search area (the number of nodes), comprising the steps of: obtaining a minimum basic unit of spatial- distance-based true cost, such as expense, time, real distance, or the like, of each link in the entire shortest path search area (the entire network); constructing a temporary shortest path that is directly connected to a starting node and a destination node with a minimum spatial distance and calculating true cost of the temporary shortest path; and applying the minimum basic unit of spatial-distance-based true cost to the true cost of the temporary shortest path.

[9] According to another aspect of the invention, there is provided a method of calculating a minimum expected cost, comprising the steps of: obtaining a minimum basic unit of spatial-distance-based true cost; searching for a node that is directly connected to an immediate previous search node and not included both in a search- completed node set and a temporary shortest path among the nodes connected between a starting node and a destination node; and adding true cost (from the starting node) to a search node and the value of spatial distance from the search node to the destination node multiplied by the minimum basic unit of spatial-distance-based true cost. [10] According to another aspect of the invention, there is provided a method of searching for a shortest path comprising the steps of: obtaining a minimum basic unit of spatial-distance-based true cost within the reduced search area described above or the entire network; calculating a minimum expected cost using the obtained minimum basic unit of spatial-distance-based true cost; and iteratively comparing the minimum expected cost with the true cost of the temporary shortest path.

Advantageous Effects

[11] As described above, the present invention is effective in that the search area for a shortest path is minimized and a shortest path to the destination node is correctly searched in a speedy way as well. Furthermore, since a basic unit based on spatial distance is used, searching can be performed not only for the time distance, but also for any kind of costs (loads) of a path, such as real distance, expense, or the like. If the travel time is used as the cost, the present invention can be applied to the change of costs (loads) according to the change of time interval, so that it is effective in that a dynamic shortest path search is allowed. Brief Description of the Drawings

[12] Further objects and advantages of the invention can be more fully understood from the following detailed description taken in conjunction with the accompanying drawings in which:

[13] FIGS. 1 to 4 are a flowchart illustrating a method of searching for a shortest path using a minimum basic unit of spatial-distance-based time distance according to an embodiment of the invention;

[14] FIGS. 5 and 6 are a flowchart illustrating a method of constructing a temporary shortest path having a minimum spatial distance according to an embodiment of the invention; and

[15] FIG. 7 is a view showing a virtual network for explaining the present invention.

Mode for the Invention

[16] Hereinafter, the method of searching for a shortest path using the method of limiting a search area according to the present invention will be described in detail with reference to the accompanying drawings.

[17] The embodiment described below is implemented through a general computer system, a car navigation system, or the like, which comprises, as publicized, a command input unit, such as a keyboard, a mouse, a touchpad, or the like, for selecting a starting and a destination nodes, a memory unit for recording path information of a plurality of nodes, an arithmetic unit for searching for a shortest path from the starting node to the destination node using the information in the memory unit according to inputted operational control signals. The configuration of such systems is apparent to those skilled in the art that details thereof will not be described. The embodiment described below relates to the process of determining a starting node and a destination node through the command input unit and operating the arithmetic unit with reference to the content of the memory unit, so that the arithmetic unit, i.e., the subject of the operation, will not be described below.

[18] FIGS. 1 to 4 are a flowchart illustrating a method of searching for a shortest path using a minimum basic unit of spatial-distance-based time distance according to an embodiment of the invention. In the embodiment of the present invention, time distance, i.e., actual travel time, is used as a true cost.

[19] <Step 101>

[20] All of the nodes (pi, p2,M. ..., pn) in a search area are inserted into a set

[21] <Step 102>

[22] The minimum value is selected among values of time distance divided by spatial distance of all connected links. The minimum value is determined as a minimum basic unit of spatial-distance-based time distance (Min_Unit) for limiting the search area.

[23] Here, rdistφi, pj) denotes time distance between node pi and node pj, and sdis(pi, pj) denotes spatial distance between node pi and node pj. The spatial distance means a straight-line distance, which can be calculated from relative coordinates or absolute coordinates of pi and pj using mathematical expression 1 shown below.

[24] [Mathematical expression 1]

[25]

Figure imgf000006_0001

[26] In mathematical expression 1 described above, (Xi, Yi) is the coordinates of pi, and

(Xj, Yj) is the coordinates of pj. [27] Accordingly, the minimum basic unit of spatial-distance -based time distance (

Min_Unit) is determined by selecting the minimum value among the values of rdis(pi, pj) of all paths divided by sdis(pi, pj). [28] Since a basic unit is used in the present invention, not only a time distance shortest path, but also a real distance shortest path, a cost shortest path, or the like can be searched.

[29] <Step 103>

[30] The starting node is set to sp, and the destination node is set to ep.

[31] <Step 104> [32] A temporary shortest path is constructed with directly connected nodes, where the sum of spatial distance from the starting node and spatial distance to the destination node at each of the nodes becomes the minimum, and time distance of the temporary shortest path (MINP_rdis) is calculated.

[33] The process of calculation is shown in detail in FIGS. 5 and 6, where the processing stage T is set to 0, and the starting node sp is determined as a selected node p[0] and stored in the temporary shortest path Tem_MINP[i]. Time distance of the temporary shortest path (MINP_rdis) is set to 0 Step 201.

[34] The processing stage T is incremented by 1 Step 202. A search node p[i] that is directly connected to the immediate previous selected node p[i-l] and not included in the temporary shortest path Tem_MINP[k] (k=0~i-l) is selected Step 203, where the sum of spatial distance from the starting node sp and spatial distance to the destination node ep becomes the minimum.

[35] The selected search node is stored in the temporary shortest path Tem_MINP[i], and time distance from the immediate previous search node p[i-l] to the current search node p[i] is added to the time distance of the temporary shortest path Step 204.

[36] It is determined whether the search node p[i] is the destination node ep Step 205. If the search node is the destination node ep, the time distance of the temporary shortest path is outputted Step 206 and determined as the shortest time distance (MINP_rdis). If the search node is not the destination node ep, the steps from step 202 are repeated.

[37] <Step 105>

[38] The limited spatial distance (Lim_sdis) for reducing the search area can be calculated by dividing the time distance of the temporary shortest path (MINP_rdis) by the minimum basic unit of spatial-distance-based time distance (Min_Unit).

[39] That is, a node where the sum of spatial distance from the starting node sp and spatial distance to the destination node ep is larger than the limited spatial distance ( Lim_sdis) will never be included in the time distance shortest path that is shorter than the temporary shortest path.

[40] <Step 106>

[41] A node set NM of a search area that is reduced on the basis of the starting node sp and the destination node ep is constructed. If it is assumed that the nodes included in node set NM are npl, np2, ..., and npi, node npi included in the set NM is a node where the sum of spatial distance sdis(sp, npi) from the starting node sp and spatial distance sdis(npi, ep) to the destination node ep is smaller than the limited spatial distance (Lim_sdis).

[42] <Step 107>

[43] For the links in the node set NM of a reduced search area, a minimum basic unit of spatial-distance-based time distance (NMIN_Unit) is calculated again in the same manner as step 102.

[44] With the node set NM of a reduced search target area obtained as described above, the minimum basic unit of spatial-distance-based time distance (NMIN_Unit), and the shortest time distance (MINP_rdis) calculated from the temporary shortest path, the shortest path from the starting node sp to the destination node ep is searched for.

[45] <Step 108>

[46] The processing stage T is set to 0, and time distance c[i] up to the processing stage

T is set to 0. The starting node sp is stored in the search-completed node set FN[i] of stage T and the search node np[i] and the temporary shortest path node (Tem_MINP [i]) are set to the starting node sp.

[47] <Step 109>

[48] The processing stage T is incremented by 1 (i <= i+1).

[49] <Step l lO>

[50] A node that is directly connected to the immediate previous search node np[i-l] and not included in the search-completed node set FN[i] and the temporary shortest path node (Tem_MINP[k] (k=0~i-l)) is searched for and determined as the search node np

[i].

[51] <Step l l l>

[52] If a search node np[i] matching to the conditions is not found, the process goes to step 117.

[53] <Step l l2>

[54] The searched node np[i] is stored in the search-completed node set FN[i], and time distance rdis(np[i-l], np[i]) from the immediate previous search node np[i-l] to the current search node np[i] is added to time distance c[i-l] from the starting node to the immediate previous search node np[i-l], thereby updating the time distance c[i].

[55] Minimally expected time distance (c_dis) is a distance to the destination node that can be expected in minimum in the current processing stage T which is calculated by adding the updated time distance c[i] and spatial distance sdis(np[i], ep) from the search node np[i] to the destination node ep multiplied by the minimum basic unit of spatial-distance-based time distance (NMIN_Unit).

[56] c_dis = c[i] + sdis(np[i] , ep) x NMINJJnit

[57] Here, c_dis denotes minimally expected time distance, c[i] denotes time distance constructed from the starting node sp to the search node np[i] of stage T, sdis(np[i], ep) denotes spatial distance from the search node of stage T to the destination node ep , and NMIN_Unit denotes the minimum basic unit of spatial-distance-based time distance.

[58] <Step l l3>

[59] If the minimally expected time distance (c_dis) is larger than the shortest time distance (MINP_rdis), the process goes to step 110. [60] <Step l l4>

[61] If the minimally expected time distance (c_dis) is smaller than the shortest time distance (MINP_rdis), the search node (np[i]) is stored in the temporary shortest path node (Tem_MINP[i]). [62] <Step l l5>

[63] If the search node (np[i]) is not the destination node (ep) in step 114, the process goes to step 109. [64] <Step l l6>

[65] If the search node (np[i]) is the destination node (ep) in step 114, time distance c[i] up to the current stage is determined as the shortest time distance (MINP_rdis), the current stage T is determined as the last stage Fi of the shortest path, the temporary shortest path (Temp_MINP[i]) from stage 0 to the current stage Fi is converted to the shortest path MINP[i], and the process goes to step 110. [66] <Step l l7>

[67] All the nodes in the search-completed node set FN[i] in the current stage T are removed (a null set) (FN[i] = { }), and the stage is decremented by 1 (i <= i-1). [68] <Step l l8>

[69] If stage Tis not 0, the process goes to step 110.

[70] <Step l l9>

[71] The shortest path set (MINP[k] (k=0~Fi)) is outputted, and the shortest time distance (MINP_rdis) is outputted. [72] If the travel time of a path is given according to an update interval (10 minutes, 5 minutes, or the like), the steps from step 103 are repeated within the same time update interval. When the update interval is over, the steps from step 102 are repeated, and thus the shortest travel time path can be efficiently searched for even in a dynamic manner.

[73] Embodiment

[74] FIG. 7 is a view of a virtual network showing node numbers, connection relations between nodes, and time distances. [75] The node set M of the search area in the virtual network of FIG. 7 is shown below

(step 101).

[76] M = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

[77] Table 1 shows spatial distances calculated from the relative coordinates of the nodes in the virtual network. [78] [Table 1]

Figure imgf000010_0001

[80] Table 2 shows time-distance values of directly connected paths divided by spatial- distance.

[81] [Table 2] [82]

Figure imgf000010_0002

[83] The minimum value among the values of time-distance divided by spatial-distance is 0.8929 of the path connecting node 4 to node 1 and the path connecting node 3 to node 2, which becomes the minimum basic unit of spatial-distance-based time distance for limiting the search area (step 102).

[84] Then, the starting node is set to node 5 (sp=5), and the destination node is set to node 9 (ep=9) (step 103). [85] The temporary shortest path and the shortest time distance, where the sum of spatial distances from the starting node (node 5) to the destination node (node 9) becomes the minimum, are obtained as described below (step 104).

[86] The nodes directly connected to the starting node (node 5) are nodes 2, 6, 7, 10, and 11. Among these nodes, the node where the sum of spatial distance from the starting node (node 5) and spatial distance to the destination node (node 9) becomes the minimum is node 7 (the sum of spatial distances is total 5.16). Then, the shortest time distance MINP_rdis is 3.8 of the time distance (rdis(5, 7)) from node 5 to node 7, and the temporary shortest path becomes Tem_MINP[0]=5 and Tem_MINP[l]=7.

[87] Since node 7 is not the destination node, the search is performed again at node 7. The nodes directly connected to node 7 and not included in the temporary shortest path are nodes 6, 9, and 10. Among these nodes, the node where the sum of spatial distance from the starting node (node 5) and spatial distance to the destination node (node 9) becomes the minimum is node 9 (the sum of spatial distances is total 5.10). The temporary shortest path becomes Tem_MINP[0]=5, Tem_MINP[l]=7, and Tem_MINP[2]=9, and the shortest time distance MINP_rdis becomes 3.8 + 3.2 = 7.0.

[88] The limited spatial distance (Lim_sdis) for reducing the search area is MINP_rdis/ MinJJnit, i.e., 7.0 / 0.8929 = 7.84 (step 105). [89] The node set NM within the limited spatial distance includes nodes where the sum of spatial distance from the starting node sp and spatial distance to the destination node ep is smaller than the limited spatial distance 7.84 (step 106).

[90] NM ={5, 6, 7, 8, 9, 10, 11, 13} [91] For reference, Table 3 shows the nodes that are included in the node set NM, among the entire nodes, within the limited spatial distance.

[92] [Table 3] [93]

Figure imgf000011_0001

[94] The minimum basic unit of spatial-distance -based time distance NMIN_Unit for searching for the shortest path obtained from the set NM in the same manner as step 2 is 1.025 (step 107).

[95] The search stage T is set to 0, the time distance at the starting node c[0] is set to 0, the search-completed node set FN[O] is set to 5 (sp), the temporary shortest path Tem_MINP[0] is set to 5 (sp), and the search node np[0] is set to 5 (sp) (step 108). [96] The stage Tis incremented by 1 (step 109).

[97] i = i + 1 (i = 1)

[98] The nodes directly connected to node 5, i.e., np[0], not included in the temporary shortest path node (Tem_MINP[0]=5), and not included in the search-completed node set (FN[0]={5}) are nodes 6, 7, 10, and 11. Among these nodes, node 6 is selected (an arbitrary node can be selected) (step 110). [99] np[l] = 6

[100] The selected node 6 is inserted in the search-completed node set (FN[1]={6}), and the time distance c[l] and the minimally expected time distance (c_dis) are calculated as shown below (step 112).

[101] c[l] = c[0] + rdis(np[0], np[l]) = 0 + rdis(5, 6) = 0 + 4.1 = 4.1

[102] c_dis = c[l] + sdis(np[l], ep) NMINJJnit = 4.1 + sdis(6, 9) 1.025 = 7.34

[103] Since the minimally expected time distance 7.34 is larger than the shortest time distance 7.0, the process goes to step 110 (step 113). [104] The nodes directly connected to node 5, i.e., np[0], not included in the temporary shortest path node (Tem_MINP[0]=5), and not included in the search-completed node set (FN[1]={6}) are nodes 7, 10, and 11. Among these nodes, node 7 is selected (step

110).

[105] np[l] = 7

[106] The selected node 7 is inserted in the search-completed node set (FN[1]={6, 7}), and the time distance c[l] and the minimally expected time distance (c_dis) are calculated as shown below (step 112).

[107] c[l] = c[0] + rdis(np[0] , np[l]) = 0 + rdis(5 , 7) = 0 + 3.8 = 3.8

[108] c_dis = c[l] + sdis(np[l], ep) x NMINJJnit = 3.8 + sdis(7, 9) x 1.025 = 5.44

[109] Since the minimally expected time distance 5.44 is smaller than the shortest time distance 7.0 (step 113), the search node is stored in the temporary shortest path (step

114).

[110] Tem_MINP[l] = 7

[111] Since the search node 7 is not the destination node 9, the process goes to step 109

(step 115).

[112] The stage T is incremented by 1 (step 109).

[113] i = i + l (i = 2)

[114] The nodes directly connected to node 7, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[l]=7), and not included in the search-completed node set (FN[2]={ }) are nodes 6, 9, and 10. Among these nodes, node 6 is selected (step 110). [115] np[2] = 6 [116] The selected node 6 is inserted in the search-completed node set (FN[2]={6}), and the time distance c[2] and the minimally expected time distance (c_dis) are calculated as shown below (step 112).

[117] c[2] = c[l] + rdis(np[l], np[2]) = 3.8 + rdis(7,6) = 3.8 + 1.5 = 5.3

[118] c_dis = c[2] + sdis(np[2], ep) xNMINJJnit = 5.3 + 3.16 x 1.025 = 8.54

[119] Since the minimally expected time distance 8.54 is larger than the shortest time distance 7.0, the process goes to step 110 (step 113). [120] The nodes directly connected to node 7, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[l]=7), and not included in the search-completed node set (FN[2]={6}) are nodes 9 and 10. Among these nodes, node

9 is selected (step 110). [121] np[2] = 9

[122] The selected node 9 is inserted in the search-completed node set (FN[2]={6, 9}), and the time distance c[2] and the minimally expected time distance c_dis are calculated as shown below (step 112).

[123] c[2] = c[l] + rdis(np[l], np[2]) = 3.8 + rdis(7,9) = 3.8 + 3.2 = 7.0

[124] c_dis = c[2] + sdis(np[2], ep) xNMINJJnit = 7.0 + (0 x 1.025) = 7.0

[125] Since the minimally expected time distance 7.0 is equal to the shortest time distance

7.0 (step 113), the search node is stored in the temporary shortest path (step 114). [126] Tem_MINP[2] = 9

[127] Since search node 9 is the destination node (step 115), the shortest time distance (

MINP_rdis) becomes 7.0, i.e., the time distance c[2]. Since the current stage T is 2, the final stage Fi of the shortest path becomes 2. The temporary shortest path from stages 0 to Fi is converted to the shortest path (step 116), and the process goes to step

110.

[128] MINP[O] = Tem_MINP[0] =5

[129] MINP[I] = Tem_MINP[l] =7

[ 130] MINP[2] = Tem_MINP[2] =9

[131] The node directly connected to node 7, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[l]=7) up to the immediate previous stage, and not included in the search-completed node set (FN[2]={6, 9}) is node 10 (step 110). [132] np[2] = 10

[133] Node 10 is inserted in the search-completed node set (FN[2]={6, 9, 10}), and the time distance c[2] and the minimally expected time distance (c_dis) are calculated as shown below (step 112).

[134] c[2] = c[l] + rdis(np[l], np[2]) = 3.8 + rdis(7,10) = 3.8 + 2.1 = 5.9

[135] c_dis = c[2] + sdis(np[2], ep) xNMINJJnit = 5.9 + (1.41 x 1.025) = 7.35 [136] Since the minimally expected time distance 7.35 is larger than the shortest time distance 7.0, the process goes to step 110 (step 113). [137] A node directly connected to node 7, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[l]=7) up to the immediate previous stage, and not included in the search-completed node set (FN[2]={6, 9, 10}) does not exist, and thus the process goes to step 117 (steps 110 and 111). [138] The search-completed node set in the current stage (i = 2) is set to a null set (FN [2]

={ }), and the stage is decremented by 1 (step 117). [139] i = i - l (i = l)

[140] Since stage Tis not 0, the process goes to step 110 (step 118).

[141] The nodes directly connected to node 5, i.e., np[0], not included in the temporary shortest path node (Tem_MINP[0]=5) up to the immediate previous stage, and not included in the search-completed node set (FN[1]={6, 7}) are nodes 10 and 11. Among these nodes, node 10 is selected (step 110). [142] np[l] = 10

[143] The selected node 10 is inserted in the search-completed node set (FN[1]={6, 7,

10}), and the time distance c[l] and the minimally expected time distance (c_dis) are calculated as shown below (step 112).

[144] c[l] = c[0] + rdis(np[0] , np[l]) = 0 + rdis(5, 10) = 0 + 4.1 = 4.1

[145] c_dis = c[l] + sdis(np[l], ep) xNMINJJnit = 4.1 + 1.41 xl.025 = 5.55

[146] Since the minimally expected time distance 5.55 is smaller than the shortest time distance 7.0, the search node is stored in the temporary shortest path (step 114). [147] Tem_MINP[l] = 10

[148] Since the search node is not the destination node, the stage is incremented by 1

(step 109).

[149] i = i + l (i = 2)

[150] The nodes directly connected to node 10, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[ I]=IO) up to the immediate previous stage, and not included in the search-completed node set (FN[2]={ }) are nodes 7, 9 and 13. Among these nodes, node 7 is selected (step 110). [151] np[2] = 7

[152] The selected node 7 is inserted in the search-completed node set (FN[2]={7}), and the time distance c[2] and the minimally expected time distance (c_dis) are calculated as shown below (step 112).

[153] c[2] = c[l] + rdis(np[l], np[2]) = 4.1 + rdis(10, 7) = 4.1 + 2.1 = 6.2

[154] c_dis = c[2] + sdis(np[2], ep) xNMINJJnit = 6.2 + 2.00 x 1.025 = 8.25

[155] Since the minimally expected time distance 8.25 is larger than the shortest time distance 7.0, the process goes to step 110 (step 113). [156] The nodes directly connected to node 10, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[ I]=IO) up to the immediate previous stage, and not included in the search-completed node set (FN[2]={7}) are nodes 9 and 13. Among these nodes, node 9 is selected (step 110).

[157] np[2] = 9

[158] The selected node 9 is inserted in the search-completed node set (FN[2]={7, 9}), and the time distance c[2] and the minimally expected time distance c_dis are calculated as shown below (step 112).

[159] c[2] = c[l] + rdis(np[l], np[2]) = 4.1 + rdis(10, 9) = 4.1 + 2.8 = 6.9

[160] c_dis = c[2] + sdis(np[2], ep)xNMIN_Unit = 6.9 + 0 x 1.025 = 6.9

[161] Since the minimally expected time distance 6.9 is smaller than the shortest time distance 7.0, the search node is stored in the temporary shortest path (step 114).

[162] Tem_MINP[2] = 9

[163] Since the search node 9 is the destination node (step 115), the shortest time distance

(MINP_rdis) is converted to 6.9, i.e., the time distance c[2]. Since the current stage T is 2, the final stage Fi of the shortest path becomes 2. The temporary shortest path from stages 0 to Fi is converted to the shortest path (step 116), and the process goes to step 110.

[164] MINP[O] = Tem_MINP[0] =5

[165] MINP[I] = Tem_MINP[l] =10

[166] MINP[2] = Tem_MINP[2] =9

[167] The node directly connected to node 10, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[ I]=IO) up to the immediate previous stage, and not included in the search-completed node set (FN[2]={7, 9}) is node 13 (step 110).

[168] np[2] = 13

[169] Node 13 is inserted in the search-completed node set (FN[2]={7, 9, 13}), and the time distance c[2] and the minimally expected time distance c_dis are calculated as shown below (step 112).

[170] c[2] = c[l] + rdis(np[l], np[2]) = 4.1 + rdis(10, 13) = 4.1 + 2.0 = 6.1

[171] c_dis = c[2] + sdis(np[2], ep)xNMIN_Unit = 6.1 + 2.24 x 1.025 = 8.40

[172] Since the minimally expected time distance 8.40 is larger than the shortest time distance 6.9, the process goes to step 110 (step 113).

[173] A node directly connected to node 10, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[ I]=IO) up to the immediate previous stage, and not included in the search-completed node set (FN[2]={7, 9, 13}) does not exist, and thus the process goes to step 117 (steps 110 and 111).

[174] The search-completed node set in the current stage (i = 2) is set to a null set (FN [2] ={ }), and the stage is decremented by 1 (step 117). [175] i = i - l (i = l)

[176] Since stage Tis not 0, the process goes to step 110 (step 118).

[177] The node directly connected to node 5, i.e., np[0], not included in the temporary shortest path node (Tem_MINP[0]=5) up to the immediate previous stage, and not included in the search-completed node set (FN[1]={6, 7, 10}) is node 11 (step 110). [178] np[l] = l l

[179] Node 11 is inserted in the search-completed node set (FN[1]={6, 7, 10, 11 }), and the time distance c[l] and the minimally expected time distance c_dis are calculated as shown below (step 112).

[180] c[l] = c[0] + rdis(np[0] , np[l]) = 0 + rdis(5 , 11) = 0 + 2.8 = 2.8

[181] c_dis = c[l] + sdis(np[l], ep) xNMINJJnit = 2.8 + 3.61 xl.025 = 6.50

[182] Since the minimally expected time distance(c_dis) 6.50 is smaller than the shortest time distance 6.9, the search node is stored in the temporary shortest path (step 114). [183] Tem_MINP[l] = 11

[184] Since the search node is not the destination node, the stage is incremented by 1

(step 109).

[185] i = i + l (i = 2)

[186] The node directly connected to node 11, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[ I]=IO) up to the immediate previous stage, and not included in the search-completed node set (FN[2]={ }) is node

13 (step 110). [187] np[2] = 13

[188] Node 13 is inserted in the search-completed node set (FN[2]={ 13}), and the time distance c[l] and the minimally expected time distance c_dis are calculated as shown below (step 112).

[189] c[2]=c[l] + rdis(np[l], np[2])=2.8 + rdis(l l, 13) = 2.8 + 3.6 = 6.4

[190] c_dis = c[2] + sdis(np[l], ep) xNMINJJnit = 6.4 + 2.24 xl.025 = 8.70

[191] Since the minimally expected time distance 8.70 is larger than the shortest time distance 6.9, the process goes to step 110 (step 113). [192] A node directly connected to node 11, i.e., np[l], not included in the temporary shortest path nodes (Tem_MINP[0]=5, Tem_MINP[ I]=IO) up to the immediate previous stage, and not included in the search-completed node set (FN[2]={ 13}) does not exist, and thus the process goes to step 117 (steps 110 and 111). [193] The search-completed node set in the current stage (i = 2) is set to a null set (FN [2]

={ }), and the stage is decremented by 1 (step 117). [194] i = i - l (i = l)

[195] Since stage Tis not 0, the process goes to step 110 (step 118). [196] A node directly connected to node 5, i.e., np[0], not included in the temporary shortest path node (Tem_MINP[0]=5) up to the immediate previous stage, and not included in the search-completed node set (FN[1]={6, 7, 10, 11 }) does not exist, and thus the process goes to step 117 (steps 110 and 111).

[197] The search-completed node set in the current stage (i = 1) is set to a null set (FN[I]

={ }), and the stage is decremented by 1 (step 117).

[198] i = i - 1 (i = 0)

[199] Since stage i is 0 (step 118), the shortest path MINP[k] (k=0~Fi) and the shortest time distance MINP_rdis are outputted.

[200] The shortest path is MINP[O] = 5, MINP[I] = 10, and MINP[2] = 9, and

[201] the shortest time distance MINP_rdis is 6.9.

[202]

Claims

Claims
[1] A method of limiting a search area for searching for a shortest path by an arithmetic unit using information in memory according to inputted operational control signals, the arithmetic unit making use of a command input unit for selecting a source node and a destination node, such as a keyboard, mouse, touchpad, or the like, and a memory unit for recording path information of a plurality of nodes, the method comprising the following steps: a first step of allowing the arithmetic unit of determining a minimum value among values of a true cost of each link in a target network divided by a spatial distance as a minimum basic unit of spatial-distance-based true cost; a second step of allowing the arithmetic unit of constructing a temporary shortest path including directly connected nodes, where a sum of spatial distance from a starting node and spatial distance to a destination node becomes minimum, calculating a true cost of the constructed temporary shortest path, and determining the true cost as a shortest cost; a third step of obtaining a limited spatial distance by dividing the shortest cost calculated in the second step by the minimum basic unit of spatial-distance-based true cost obtained in the first step; and a fourth step of limiting the search area by selecting nodes where the sum of spatial distance from the starting node and spatial distance to the destination node is smaller than the limited spatial distance obtained in the third step.
[2] The method according to claim 1, wherein the true cost is selected from time, expense and real distance.
[3] A method of obtaining a minimum expected cost by an arithmetic unit using information in memory according to inputted operational control signals, the arithmetic unit making use of a command input unit for selecting a source node and a destination node, such as a keyboard, mouse, touchpad, or the like, and a memory unit for recording path information of a plurality of nodes, the method comprising the following steps: a first step of determining a minimum value among values of a true cost divided by a spatial distance as a minimum basic unit of spatial-distance -based true cost; and a second step of calculating the minimum expected cost desired to be known for a certain specific node by adding a value of spatial distance from the specific node to a destination node multiplied by the minimum basic unit of spatial- distance-based true cost obtained in the first step to a true cost from a starting node to the specific node. [4] A method of searching for a shortest path by an arithmetic selected from one unit using information in memory according to inputted operational control signals, the arithmetic unit making use of a command input unit for selecting a source node and a destination node, such as a keyboard, a mouse, a touchpad, or the like, and a memory unit for recording path information of a plurality of nodes, the method comprising the following steps: a first step of obtaining a minimum value among values of a true cost of each link in a network divided by a spatial distance and determining the obtained value as a minimum basic unit of spatial-distance-based true cost; a second step of setting a processing stage to 0, setting a real distance up to the processing stage to 0, inserting a starting node into a search-completed node set of the processing stage 0, and setting a search node and a temporary shortest path node of the processing stage 0 to the starting node; a third step of incrementing the processing stage by 1; a fourth step of searching for a certain node that is directly connected to the search node of an immediate previous processing stage and not included in the search-completed node set and the temporary shortest path node of the current processing stage, and determining the certain node as the search node; a fifth step, if a search node does not exist in the fourth step, of jumping to a ninth step; a sixth step, if a search node exists in the fourth step, of storing the search node into the search-completed node set of the current processing stage, updating the true cost by adding a true cost from the search node of the immediate previous processing stage to the search node of the current processing stage to a true cost of the immediate previous processing stage, and calculating a minimum expected cost by adding the updated true cost and spatial distance from the search node of the current processing stage to a destination node multiplied by the minimum basic unit of spatial-distance-based true cost obtained in the first step; a seventh step of comparing the calculated minimum expected cost with a shortest cost, and returning to the third step if the calculated minimum expected cost is larger than the shortest cost, or storing the search node into the temporary shortest path if the calculated minimum expected cost is smaller than the shortest cost; an eighth step, in the case where the minimum expected cost is smaller than the shortest cost, of returning to the fourth step if the search node is not the destination node, and if the search node is the destination node, determining the true cost updated up to the current stage as the shortest cost, converting the nodes stored in the temporary shortest path up to the current stage into the shortest path, and returning to the fourth step; the ninth step, in the case where a node matching to the conditions does not exist, of removing all the nodes in the search-completed node set of the current stage and decrementing the processing stage by 1 ; and a tenth step of returning to the fourth step if the processing stage is not 0, or outputting the calculated shortest time distance and the nodes in the shortest path if the processing stage is 0.
[5] The method according to claim 4, wherein the method of searching for a shortest path uses the method of limiting a search area claimed in claims 1 to 2 and obtains the minimum basic unit of spatial-distance-based true cost from the nodes limited in the fourth step.
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