Indoor Routing on Logical Network Using Space Semantics
Abstract
:1. Introduction
2. Background
3. Generic Space Classification for Routing
 Opening. This is a transition space which connects one space with another. These spaces (e.g., an entrance) can connect the outdoor space as well.
 Navigable Unit (NU). This is a space in which users (e.g., pedestrians) can move freely (e.g., walk or drive) without crossing any opening.
 Vertical Unit (VU). VU is a subclass of NU in which pedestrians can move (or be transported) in vertical directions (i.e., up and down) along the same slope.
 Horizontal Unit (HU). This is a subclass of NU in which pedestrians can move in horizontal directions.
 Horizontal Connector (HC). An HC is an HU that connects with at least two other HUs.
 Vertical Connector (VC). A VC is an HU that connects at least two other different NUs, and at least one of them is a VU.
 End. End is a subtype of HU that is connected with one NU at most.
4. Routing Criteria Based on Space Semantics
 Fewest Navigable Unit (Fewest NU): $min(\sum w\left({n}_{i}\right)),\phantom{\rule{3.33333pt}{0ex}}s.t.\phantom{\rule{3.33333pt}{0ex}}C\left({n}_{i}\right)=NU,\phantom{\rule{3.33333pt}{0ex}}and\phantom{\rule{3.33333pt}{0ex}}W=\{w\left({n}_{i}\right)=1,\phantom{\rule{3.33333pt}{0ex}}i\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1,\dots ,M\}$.
 Fewest Horizontal Connector (Fewest HC): $min(\sum w\left({n}_{i}\right)),\phantom{\rule{3.33333pt}{0ex}}s.t.\phantom{\rule{3.33333pt}{0ex}}W=\{\{w\left({n}_{i}\right)=1\phantom{\rule{3.33333pt}{0ex}}where\phantom{\rule{3.33333pt}{0ex}}C\left({n}_{i}\right)=HC\},\{w\left({n}_{i}\right)=0\},\phantom{\rule{3.33333pt}{0ex}}i\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1,\dots ,M\}$.
 Fewest Vertical Unit (Fewest VU): $min(\sum w\left({n}_{i}\right)),\phantom{\rule{3.33333pt}{0ex}}s.t.\phantom{\rule{3.33333pt}{0ex}}W=\{\{w\left({n}_{i}\right)=1\phantom{\rule{3.33333pt}{0ex}}where\phantom{\rule{3.33333pt}{0ex}}C\left({n}_{i}\right)=VU\},\{w\left({n}_{i}\right)=0\},\phantom{\rule{3.33333pt}{0ex}}i\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1,\dots ,M\}$.
 Central Horizontal Connector (Central HC): $min(\sum w\left({n}_{i}\right)),\phantom{\rule{3.33333pt}{0ex}}s.t.\phantom{\rule{3.33333pt}{0ex}}W=\{\{w\left({n}_{i}\right)=10,000centrality\phantom{\rule{3.33333pt}{0ex}}where\phantom{\rule{3.33333pt}{0ex}}C\left({n}_{i}\right)=HC\},\{w\left({n}_{i}\right)=10,000\},i\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1,\dots ,M\}$.
 Horizontal Connector Prior (HC Prior): $min(\sum w\left({n}_{i}\right)),\phantom{\rule{3.33333pt}{0ex}}s.t.\phantom{\rule{3.33333pt}{0ex}}W=\{\{w\left({n}_{i}\right)=1\phantom{\rule{3.33333pt}{0ex}}where\phantom{\rule{3.33333pt}{0ex}}C\left({n}_{i}\right)=HC\},\{w\left({n}_{i}\right)=10,000\},\phantom{\rule{3.33333pt}{0ex}}i\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1,\dots ,M\}$.
 Vertical Unit Prior (VU Prior): $min(\sum w\left({n}_{i}\right)),\phantom{\rule{3.33333pt}{0ex}}s.t.\phantom{\rule{3.33333pt}{0ex}}W=\{\{w\left({n}_{i}\right)=1+\Delta \phantom{\rule{3.33333pt}{0ex}}where\phantom{\rule{3.33333pt}{0ex}}C\left({n}_{i}\right)=VU\},\{w\left({n}_{i}\right)=10,000\},\phantom{\rule{3.33333pt}{0ex}}i\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1,\dots ,M\}$.
5. Routing Procedure
Algorithm 1 Derive edge weights from node weights in a logical network. 
Input: A logical network G, the values Ws of node weights. Output: The logical network G where the edges have been weighted in light of Ws.

Algorithm 2 Compute logical paths with ordered criteria in a priority list on a logical network. 
Input: A prioritized list of ordered routing criteria F, a logical network N. Output: The set of logical path(s) $Sp$.

6. Experiments
 p1: 1END, 64HC, 62HC, 72HC, 71VC, 54Stair, 88VC, 90HC, 70HC, 42HC;
 p2: 1END, 64HC, 62HC, 87HC, 86VC, 61Ele, 89VC, 90HC, 70HC, 42HC;
 p3: 1END, 64HC, 62HC, 87HC, 76HC, 74VC, 58Ele, 69VC, 70HC, 42HC.
 The sequence of r1 is 130HC, 10HC, 30HC, 31HC, 32HC, 52HC, 27HC, 122HC, 97HC, 98HC, 79HC, 93HC.
 The sequence of r2 is 130HC, 10HC, 33HC, 34HC, 118HC, 42HC, 80HC, 84HC, 85HC, 86HC, 109HC, 93HC.
7. Discussions
8. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Type  Constraint  HC  VC  VU  

EL  ES  ST  
Minimizing specific types  Fewest NU  1  1  1  1  1 
Fewest HC  1  0  0  0  0  
Fewest VU  0  0  1  1  1  
Fewest EL  0  0  1  10,000  10,000  
Fewest ES  0  0  10,000  1  10,000  
Fewest ST  0  0  10,000  10,000  1  
Fewest EL&ES  0  0  1  1  10,000  
Fewest EL&ST  0  0  1  10,000  1  
Fewest ES&ST  0  0  10,000  1  1  
Setting priority to specific types  Central HC  10,000Centrality  10,000  10,000  10,000  10,000 
HC Prior  1  10,000  10,000  10,000  10,000  
VU Prior  10,000  10,000  1 + $\Delta $  1 + $\Delta $  1 + $\Delta $  
EL Prior  10,000  10,000  1 + $\Delta $  10,000  10,000  
ES Prior  10,000  10,000  10,000  1 + $\Delta $  10,000  
ST Prior  10,000  10,000  10,000  10,000  1 + $\Delta $  
EL&ES Prior  10,000  10,000  1 + $\Delta $  1 + $\Delta $  10,000  
EL&ST Prior  10,000  10,000  1 + $\Delta $  10,000  1 + $\Delta $  
ES&ST Prior  10,000  10,000  10,000  1 + $\Delta $  1 + $\Delta $ 
Fewest NU  Fewest HC  Fewest VU  VU Prior  HC Prior  Central HC 

p1, p2, p3  p1, p2, p3  p1, p2, p3  p1, p2  p3  p1 
Fewest NU  Fewest HC  HC Prior  Central HC 

r1, r2  r1, r2  r1, r2  r1 
StartTarget  Path Set 

1–82  A1: 1END, 64HC, 95HC, 91VC, 53Esc, 96VC, 100HC, 68HC, 82HC A2: 1END, 64HC, 95HC, 85HC, 84VC, 56Esc, 67VC, 68HC, 82HC A3: 1END, 64HC, 62HC, 87HC, 76HC, 73VC, 57Stair, 81VC, 82HC A4: 1END, 64HC, 95HC, 85HC, 83VC, 55Ele, 66VC, 68HC, 82HC A5: 1END, 64HC, 95HC, 94VC, 65Esc, 98VC, 100HC, 68HC, 82HC A6: 1END, 64HC, 95HC, 93VC, 60Stair, 99VC, 100HC, 68HC, 82HC A7: 1END, 64HC, 95HC, 92VC, 52Ele, 97VC, 100HC, 68HC, 82HC 
1–26  B1: 1END, 64HC, 95HC, 91VC, 53Esc, 96VC, 100HC, 68HC, 82HC, 26HC B2: 1END, 64HC, 95HC, 85HC, 84VC, 56Esc, 67VC, 68HC, 82HC, 26HC B3: 1END, 64HC, 62HC, 87HC, 86VC, 61Ele, 89VC, 90HC, 37HC, 26HC B4: 1END, 64HC, 95HC, 93VC, 60Stair, 99VC, 100HC, 68HC, 82HC, 26HC B5: 1END, 64HC, 95HC, 85HC, 83VC, 55Ele, 66VC, 68HC, 82HC, 26HC B6: 1END, 64HC, 95HC, 92VC, 52Ele, 97VC, 100HC, 68HC, 82HC, 26HC B7: 1END, 64HC, 95HC, 94VC, 65Esc, 98VC, 100HC, 68HC, 82HC, 26HC B8: 1END, 64HC, 62HC, 87HC, 76HC, 73VC, 57Stair, 81VC, 82HC, 26HC B9: 1END, 64HC, 62HC, 72HC, 71VC, 54Stair, 88VC, 90HC, 37HC, 26HC 
10–25  C1: 10END, 16HC, 72HC, 71VC, 54Stair, 88VC, 90HC, 27HC, 100HC, 68HC, 25END C2: 10END, 16HC, 72HC, 87HC, 76HC, 73VC, 57Stair, 81VC, 82HC, 68HC, 25END C3: 10END, 16HC, 72HC, 71VC, 54Stair, 88VC, 90HC, 37HC, 82HC, 68HC, 25END 
4–38  D1: 4HC, 95HC, 85HC, 84VC, 56Esc, 67VC, 68HC, 38HC D2: 4HC, 95HC, 92VC, 52Ele, 97VC, 100HC, 68HC, 38HC D3: 4HC, 95HC, 94VC, 65Esc, 98VC, 100HC, 68HC, 38HC D4: 4HC, 95HC, 85HC, 83VC, 55Ele, 66VC, 68HC, 38HC D5: 4HC, 95HC, 91VC, 53Esc, 96VC, 100HC, 68HC, 38HC D6: 4HC, 95HC, 93VC, 60Stair, 99VC, 100HC, 68HC, 38HC 
15–95  E1: 11END, 17HC, 72HC, 87HC, 76HC, 73VC, 57Stair, 81VC, 82HC, 68HC, 24END E2: 11END, 17HC, 72HC, 71VC, 54Stair, 88VC, 90HC, 27HC, 100HC, 68HC, 24END E3: 11END, 17HC, 72HC, 71VC, 54Stair, 88VC, 90HC, 37HC, 82HC, 68HC, 24END 
Start and Target Space  1–82  1–26  10–25  4–38  15–95 

Path Set  A1, A2, A3, A4, A5, A6, A7  B1, B2, B3, B4, B5, B6, B7, B8, B9  C1, C2, C3:  D1, D2, D3, D4, D5, D6  E1, E2, E3 
Fewest NU  A1, A2,A3, A4, A5, A6, A7  B1, B2, B3, B4, B5, B6, B7, B8, B9  C1, C2, C3  D1, D2, D3, D4, D5, D6  E1, E2, E3 
Fewest  
HC  A1, A2, A3, A4, A5, A6, A7  B1, B2, B3, B4, B5, B6, B7, B8, B9  C1, C2, C3  D1, D2, D3, D4, D5, D6  E1, E2, E3 
Fewest  
VU  A1, A2, A3, A4, A5, A6, A7  B1, B2, B3, B4, B5, B6, B7, B8, B9  C1, C2, C3  D1, D2, D3, D4, D5, D6  E1, E2, E3 
HC Prior  A3  B8  C2  D1, D4  E1 
VU Prior  A1, A5, A6, A7  B1, B4, B6, B7  C1, C3  D2, D3, D5, D6  E2, E3 
Central HC  A1, A5, A6, A7  B9  C3  D2, D3, D5, D6  E3 
Building  Nodes More Than 4 Degrees  All Nodes  Connector Ratio (%) 

Schiphol Airport  34  95  35.79 
MFA  45  131  34.35 
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Liu, L.; Zlatanova, S.; Li, B.; van Oosterom, P.; Liu, H.; Barton, J. Indoor Routing on Logical Network Using Space Semantics. ISPRS Int. J. GeoInf. 2019, 8, 126. https://doi.org/10.3390/ijgi8030126
Liu L, Zlatanova S, Li B, van Oosterom P, Liu H, Barton J. Indoor Routing on Logical Network Using Space Semantics. ISPRS International Journal of GeoInformation. 2019; 8(3):126. https://doi.org/10.3390/ijgi8030126
Chicago/Turabian StyleLiu, Liu, Sisi Zlatanova, Bofeng Li, Peter van Oosterom, Hua Liu, and Jack Barton. 2019. "Indoor Routing on Logical Network Using Space Semantics" ISPRS International Journal of GeoInformation 8, no. 3: 126. https://doi.org/10.3390/ijgi8030126