CLAIMS

(Antecedent basis is tracked with boxes: a term is later used as the term , mostly.)

1. A method for searching or comparing at least one site using

at least one route or route length between the at least one site and

at least one place within a transportation system, the method comprising:

(a) receiving a plurality of sites wherein each site is included in the transportation system, the plurality of sites including the at least one site;;

(b) receiving at least one representative, wherein each representative is included in the transportation system;;

(c) storing in a database at least one precomputed route or route length wherein each first precomputed route or route length comprises a description of travel within the transportation system between a site included in the plurality of sites and a representative included in the at least one representative;;

(d) receiving a request comprising the at least one place, wherein each place is included in the transportation system the at least one place including at least one start/end place;;

(e) computing the at least one route or route length,

wherein each route or route length comprises a description of travel within the transportation system between a site included in the at least one site and a place included in the at least one place,

wherein the computing comprises:

i. determining at least one nearby representative, wherein each

nearby representative:

A. is included in the at least one representative, and

B. wherein a length of travel between the nearby representative and a start/end place included in the at least one start/end place is within a threshold; and

ii. for each nearby representative included in the

at least one nearby representative retrieving from the

at least one precomputed route or route length stored in the database a second precomputed route or route length between the

nearby representative and a not nearby site, wherein the not nearby site is included in the plurality of sites;; and

(f) responding to the request with information comprising a representation of the at least one route or route length.

2. The method of Claim 1, wherein

(a) a site included in the at least one site represents a real estate property, and a place included in the at least one place represents a commute destination; or

(b) a site included in the at least one site represents a commute destination, and a place included in the at least one place represents a real estate property.

3. The method of Claim 1, wherein the request further comprises at least one of:

(a) a first departure time from a second site included in the at least one site;

(b) a first arrival deadline at a third site included in the at least one site;

(c) a second departure time from a second place included in the

at least one place ; or

(d) a second arrival deadline at a third place included in the at least one place

4. The method of Claim 1, wherein the at least one place includes:

(a) for each i in the range 2 ≤ i ≤ k‒1, for a threshold k that is even, a place P_{i};;

wherein the at least one start/end place includes:

(b) a start place P_{1} or an end place P_{k}, for the threshold k;;

wherein the computing the route or route length further comprises:

(c) receiving a first site or a last site, each included in the at least one site and

(d) using:

i. a description of travel from the first site to the start place P_{1}, or a description of travel from the end place P_{k} for the threshold k, to the last site; and

ii. for each even i in the range 2 ≤ i ≤ k ‒ 2, for the Threshold k , a description of travel from the place P_{i} to the place P_{i+1}.

5. The method of Claim 1, wherein the route or route length involves two or more sites included in the at least one site.

6. The method of Claim 1, wherein

(a) the at least one route or route length includes a

site-place route or route length;

further comprising:

(b) storing the site-place route or route length in the database;

wherein the computing further comprises:

(c) retrieving from the database the site-place route or route length.

7. The method of Claim 1, wherein

(a) the plurality of sites includes a cluster site, the cluster site representing one or more site included in the plurality of sites, the one or more site clustered based on at least one of:

i. a length of travel; or

ii. a geographical proximity, wherein the one or more site further comprises a geographical location;; or

(b) the at least one representative includes a cluster representative, the cluster representative representing one or more representative included in the at least one representative, the one or more representative clustered based on at least one of:

i. a length of travel; or

ii. a geographical proximity, wherein the one or more representative further comprises a geographical location.

8. The method of Claim 1, wherein the plurality of sites includes

at least one site connector ;;

wherein

(a) the not nearby site is included in the at least one site connector; and

(b) the computing the route or route length further comprises:

i. using a description of travel between the not nearby site and a zeroth site , wherein the zeroth site is included in the at least one site.

9. The method of Claim 1, wherein a compression list comprises one or more first precomputed route or route length, and the storing in the database the at least one precomputed route or route length further comprises compressing the compression list.

10. The method of Claim 1, wherein

(a) the storing in the database the

at least one precomputed route or route length , or

(b) the computing the at least one route or route length

further comprises:

(c) receiving a manipulation function , and

(d) applying the manipulation function to: the

at least one precomputed route or route length or the

at least one route or route length.

11. The method of Claim 10, wherein the manipulation function comprises setting to infinity a first route length included in:

(a) the at least one precomputed route or route length , or

(b) the at least one route or route length ;

the first route length being between a first real estate property and a first school , wherein

(c) the first real estate property is included in the at least one site ,

(d) the first school is included in the at least one place, and

(e) the first real estate property is outside of a zone of the first school.

12. The method of Claim 1, further comprising:

(a) receiving data about the transportation system , comprising:

i. a plurality of transportation elements ; and

ii. at least one segment length, each segment length describing a length of travel from a first transportation element to a

second transportation element , each transportation element included in the plurality of transportation elements ;; and

(b) creating a graph comprising a plurality of graph vertexes, including:

i. a plurality of transportation element vertexes, each transportation element vertex representing one of the

plurality of transportation elements ;

ii. a plurality of site vertexes , each site vertex representing one of the plurality of sites ; and

111. at least one representative vertex, each representative vertex representing one of the at least one representative ;

the graph further comprising a plurality of graph edges, including a graph edge that leads from a graph edge source vertex to a

graph edge target vertex and comprises a graph edge weight, the graph edge comprising one of:

iv. the graph edge source vertex comprising a

first transportation element vertex included in the

plurality of transportation element vertexes, the

graph edge target vertex comprising a

second transportation element vertex included in the

plurality of transportation element vertexes, and the graph edge weight representing a segment length included in the

at least one segment length, the segment length describing a length of travel from a transportation element being represented by the

first transportation element vertex to a transportation element being represented by the second transportation element vertex;

v. the graph edge source vertex and the graph edge target vertex comprising a first graph vertex and a second graph vertex in some order, the first graph vertex being included in the

plurality of site vertexes, and the second graph vertex being included in the plurality of graph vertexes, and the graph edge weight describing a length of travel between a site being represented by the first graph vertex and an entity being represented by the second graph vertex ; or vi. the graph edge source vertex and the graph edge target vertex comprising a third graph vertex and a fourth graph vertex in some order, the third graph vertex being included in the

at least one representative vertex and the fourth graph vertex being included in the plurality of graph vertexes , and the graph edge weight describing a length of travel between a representative being represented by the third graph vertex and an entity being represented by the fourth graph vertex;;

wherein the first precomputed route or route length comprises a representation of:

(c) a graph path or graph path length between a representative vertex included in the at least one representative vertex and a site vertex included in the plurality of site vertexes.

13. The method of Claim 12, wherein the plurality of graph vertexes includes a graph vertex that represents at least one of:

(a) a transit station of a public transportation vehicle,

(b) a stop of a vehicle,

(c) a turn of a vehicle,

(d) a stop of a walk, or

(e) a turn of a walk; or

wherein the plurality of transportation elements comprises a transportation element further comprising a time , and a graph vertex included in the plurality of graph vertexes represents the time.

14. The method of Claim 12, wherein the graph edge weight represents at least one of:

(a) a number of transfers among public transportation vehicles,

(b) a duration of travel,

(c) a monetary cost of travel,

(d) a duration of wait,

(e) a monetary cost of wait, or

(f) a distance of travel; or

wherein the at least one segment length comprises a segment length further comprising a transportation departure time from the first transportation element or a transportation arrival time at the second transportation element, and the graph edge weight describing a length of travel that starts at the transportation departure time or that ends at the transportation arrival time.

15. The method of Claim 12, wherein the graph path or graph path length between the representative vertex and the site vertex is obtained by applying at least one of:

(a) a Dijkstra’s shortest paths algorithm, or

(b) an A* (A star) search algorithm,

to at least one of:

(c) the graph or

(d) the graph with reversed graph edges.

16. The method of Claim 1, wherein the plurality of sites comprises:

(a) for each i in the range 1 ≤ i ≤ m, for a threshold m ≥ 1, a site S_{i};; further comprising:

(b) receiving at least one coordinate , each coordinate i in the range 1 ≤ i ≤ m, for the threshold m;;

wherein the at least one precomputed route or route length comprises:

(c) a vector v comprising, for each coordinate i included in the

at least one coordinate, a value v[i] that comprises the

first precomputed route or route length that comprises a description of travel from the nearby representative to the site S_{i}; or

(d) a vector v' comprising, for each coordinate i included in the

at least one coordinate a value v'[i] that comprises the

first precomputed route or route length that comprises a description of travel from the site S_{i} to the nearby representative.

17. The method of Claim 16, wherein

(a) the at least one coordinate includes at least two coordinates, and the storing the at least one precomputed route or route length further comprises:

laying out, for a sequence of coordinate i included in the

at least one coordinate,

i. the value v[i] or the value v'[i] ,

sequentially in the database ; or

(b) the storing the at least one precomputed route or route length further comprises:

storing a list or a hash map comprising, for at least one coordinate i included in the at least one coordinate,

i. the value v[i] or the value v'[i] ,

in the 1 database .

18. The method of Claim 16, further comprising:

for at least one first coordinate i included in the at least one coordinate,

(a) receiving a weight w_{i};;

wherein, for the first coordinate i, the storing further comprises:

(b) determining a length of travel, denoted a rs_{i}, from the

nearby representative to the < site S_{i}; and

(c) determining a length of travel, denoted a sr_{i} , from the site s_{i} to the nearby representative;;

wherein, for the first coordinate i,

(d) the value v[i] or the value v'[i]

comprises a length of travel equal to W_{i} · rs_{i} + (1 — W_{i}) · sr_{i}, for the weight W_{i} , the rs_{i}, the sr_{i}.

19. The method of Claim 16, further comprising:

for at least one second coordinate i included in the at least one coordinate,

(a) receiving a lower bound lb_{i}, an upper bound ub_{i}, and a

scaling factor sf_{i};;

wherein, for the second coordinate i, the storing further comprises:

(b) determining a length of travel, denoted a bsr_{i}, between the site S_{i} and the nearby representative;;

wherein, for the second coordinate i,

(c) the value v[i] or the value v'[i] ,

comprises a length of travel equal to: the bsr_{i} multiplied by the scaling factor sf_{i}, rounded to an integer, and capped to within a range from the lower bound lb_{i} to the upper bound ub_{i}.

20. The method of Claim 16, wherein the at least one nearby representative comprises:

(a) for each j in the range 1 ≤ j ≤ s, for a threshold s ≥ 1, a

nearby representative R_{j}

further comprising:

(b) receiving a + operation comprising calculating a first sum of a number, for one or more coordinate of a vector, with a value at the coordinate; and

(c) receiving a min operation comprising calculating, for one or more coordinate, a third minimum of a value at the coordinate across a plurality of vectors;;

wherein

(d) the at least one start/end place includes a start place, and wherein the computing the at least one route or route length further comprises: i. for each j in the range 1 ≤ j ≤ s, for the threshold s , determining a length of travel

that is a length of travel from the nearby representative R_{j} J to the start place;

wherein the at least one precomputed route or route length comprises for each j in the range 1 ≤ j ≤ s, for the threshold s , a vector that

is the vector v' wherein the nearby representative is the

nearby representative R_{j};

wherein a length of travel vector comprises, for at least one third coordinate i included in the ^{1} at least one coordinate, a value that is a length of travel included in the value [i] of the j vector at the

third coordinate i; and

ii. finding a first minimum using a first mathematical formula comprising the min operation and the + operation :

^{min}1≤j ≤s {

( the length of travel ) + ( the | length of travel vector

)},

the first minimum for at least one fifth coordinate i included in the at least one coordinate:

represents a description of travel from the site S_{i} to the

start place , and

uses the second precomputed route or route length, wherein the not nearby site is the site S_{i};; or

(e) the at least one start/end place includes an end place, and wherein the computing the at least one route or route length further comprises: i. for each j in the range 1 ≤ j ≤ s, for the threshold s ], determining a length of travel that is a length of travel from

the end place to the nearby representative R_{j};

wherein the at least one precomputed route or route length comprises, for each j in the range 1 ≤ j ≤ s, for the threshold s , a vector that

is the vector v wherein the nearby representative i is the

nearby representative R_{j} ;

wherein a length of travel vector comprises, for at least one

fourth coordinate i included in the at least one coordinate, a value that is a length of travel included in the value [I] of the vector at

the fourth coordinate i; and

ii. finding a second minimum using a second mathematical formula comprising the min operation and the + operation :

min1≤j≤s{

( the length of travel ) + ( the length of travel vector

)},

the second minimum, for at least one sixth coordinate i included in the at least one coordinate :

represents a description of travel from the end place to the site S_{i}, and

uses the second precomputed route or route length, wherein the not nearby site is the site S_{i}.

21. The method of Claim 20, wherein

(a) the calculating included in the + operation comprises at least one of:

i. a Saturation Arithmetic operation within a range from a lower bound to an upper bound,

ii. an arithmetic operation operating on an integer, or

iii. an arithmetic operation operating on a floating point number;

(b) the first mathematical formula or the

second mathematical formula further comprise at least one Vector Operation supported by hardware; or

(c) the using of the first mathematical formula or the using of the second mathematical formula further comprise: dividing calculations into a plurality of partitions , and executing the plurality of partitions in parallel.

22. The method of Claim 1, wherein the request comprises:

(a) for each i in the range 1 ≤ i ≤ q, for a threshold q ≥ 1, a

route specification L_{i} , wherein the route specification L_{i} comprises one or more place , the one or more place including

one or more start/end place;;

wherein the request further comprises:

(b) a deriver , wherein the deriver comprises an algorithm that computes a deriver output given a deriver input;;

wherein the information further comprises:

(c) the deriver output wherein the deriver input comprises a sequence

T_{1}, . . . , T_{q} for the threshold q, wherein for each i in the range 1 ≤ i ≤ q, a

T_{i} comprises a part of the information , wherein

i. the at least one place is the one or more place included in the route specification L_{i}, and

ii. the at least one start/end place is the one or more start/end place included in the route specification L_{i}.

23. The method of Claim 22, wherein the deriver comprises one of:

(a) the deriver output comprising, for a fourth site included in the

at least one site a minimum route length that is a route length equal to a fourth minimum, across i in the range 1 ≤ i ≤ q, for the threshold q, of a second route length included in theT_{i}, the second route length involving the fourth site;;

(b) receiving weights w_{1}, . . . , w_{q}, for the threshold q , as a part of the deriver input ; and the deriver output comprising, for a fifth site included in the at least one site, a weighted route length that is a route length equal to a second sum, across i in the range 1 ≤ i ≤ g, of a third route length included in the T_{i}, the third route length involving the fifth site , the third route length weighted by a weight w_{i} included in the weights w_{1}, . . . , w_{q} ;; or

(c) receiving a site S as a part of the deriver input , the site S included in the at least one site ; and the deriver output comprising, for a sixth site included in the at least one site, difference route length that is a route length equal to a difference between a fourth route length involving the sixth site and a fifth route length involving the site S , the fourth route length and the fifth route length included in the deriver input .

24. The method of Claim 1, wherein the request further comprises:

(a) a condition on: the at least one site , or a part of the information ; wherein the information further comprises a filtering of:

(b) the at least one site , or

(c) the information ,

that match the condition

25. The method of Claim 24, wherein the condition comprises at least one of:

(a) a threshold of a maximum commute duration, or a maximum walk distance;

(b) a real estate property type, or a real estate property price or size range; or

(c) a job type, or a job salary range.

26. The method of Claim 1, wherein the request further comprises:

(a) an aggregator , wherein the aggregator comprises an algorithm that computes an aggregator output given an aggregator input

wherein the information further comprises:

(b) the aggregator output, wherein the aggregator input comprises a sequence I_{1}, . . . , I_{r}, for a threshold r ≥ 1, wherein for each i in the range 1 ≤ i ≤ r, for the threshold r , an I_{i} comprises a part of the information .

27. The method of Claim 26, wherein the aggregator output comprises a centrality of a seventh site within the transportation system , the seventh site included in the at least one site .

28. The method of Claim 1, wherein the request further comprises:

(a) a cost function , wherein the cost function computes a cost function value given a cost function input , wherein the cost function input comprises: i. an exploration route length being a route length included in the information; and

(b) an exploration algorithm , wherein the exploration algorithm comprises an algorithm that computes:

i. the cost function value for at least one cost function input, and ii. an exploration output

wherein the informatiom further comprises:

(c) the exploration output .

29. The method of Claim 28, wherein

(a) the cost function is a differentiable function that depends on the exploration route length ; and

(b) the exploration algorithm comprises a gradient descent algorithm that computes a gradient of the cost function .

30. The method of Claim 1, wherein the storing or the computing further comprise applying a multi-objective optimization search based on a multi-dimensional cost

31. The method of Claim 30, wherein the multi-dimensonal cost comprises at least one of:

(a) a price or a size of a site included in the at least one site_{.}]; or

(b) a route length, a monetary cost, a wait duration, a number of vehicle transfers, or a walking distance included in: the

at least one precomputed route or route length , or the

at least one route or route length .

A computer system for searching or comparing at least one site using at least one route or route length between the at least one site and at least one place within a transportation system, the computer system comprising:

(a) one or more processor;

(b) a computer-readable storage medium storing one or more program for execution by the one or more processor ; and

(c) the one or more program comprising instructions to be executed by the

one or more processor so as to perform the method of one of: Claim 1 to Claim

31.

An apparatus for searching or comparing at least one site using at least one route or route length between the at least one site and at least one place within a transportation system, the apparatus comprising:

(a) a receiver configured to receive from a user the request ,

(b) a transmitter configured to respond to the user with a part of the information , and

(c) one or more module configured to perform the method of one of: Claim 1 to Claim 31.

34. The apparatus of Claim 33, wherein the receiver receives at least one of:

(a) the at least one place ;

(b) thecondition;

(c) the first departure time , the first arrival deadline , the

second departure time, or the second arrival deadline; or

(d) the deriver ;;

wherein the Transmitter further responds with at least one of:

(e) a geographical location of: a place included in the at least one place , or a site included in the at least one site , rendered on a map;;

(f) a departure time or an arrival time for: a place included in the

at least one place or a site included in the at least one site ;;

(g) a summary of a site included in the at least one site; or at least one of: a name of the site, an address of the site, a price of the site, or a size of the site;; (h) a summary of a cluster of nearby sites , wherein the cluster of nearby sites comprises sites included in the at least one site clustered based on a length of travel or a geographical proximity;;

(i) a rendering of the cluster of nearby sites , a size of the rendering being correlated with a number of sites in the cluster of nearby sites ;;

(j) a stacking of sites, each eighth site included in the at least one site , the stacking in a z-index order of a route length that is included in the information and involves the eighth site , shorter route length higher up the stacking, rendered on a map;;

(k) a summary of the route or route length ; or a part of the

route or route length , the part including at least one of: i. a route: length, duration, monetary cost, speed, or wait duration; ii. a name of: a vehicle, a vehicle road, a walking path, a stop, a turn, or a transit station of a public transportation vehicle; or iii. a geographical location of: a monetary cost, a speed, a wait duration, a vehicle, a vehicle road, a walking path, a stop, a turn, or a transit station of a public transportation vehicle;;

(l) a histogram of a route length included in the information , the route length involving a site, across the at least one site ; or a heatmap of the route length across the at least one site rendered on a map;;

(m) the minimum route length ; a histogram of the minimum route length across the at least one site ; or a heatmap of the minimum route length across the at least one site; rendered on a map;;

(n) the weighted route length ; a histogram of the weighted route length across the at least one site or a heatmap of the weighted route length across the at least one site rendered on a map;;

(o) the difference route length ; a histogram of the difference route length across the at least one site or a heatmap of the difference route length across the at least one site; rendered on a map;;

(p) a rendering of the deriver output ;;

(q) a ninth site that minimizes a sixth route length included in the information , the sixth route length involving the ninth site , minimized across the at least one site , constrained by a threshold on a monetary cost of travel;;

(r) at least one of: the above item (e) to item (q), constrained by the condition;;

or

(s) a top list comprising sites included in the at least one site , wherein

i. each tenth site included in the top list and

ii. a seventh route length that is included in the information and involves the tenth site,

satisfy the condition the top list sorted by the seventh route length .