Finding the Shortest Path with Vertex Constraint over Large Graphs

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/8728245/figures/8728245.fig.003a.svgz" name="8728245.fig.003a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Query graph <svg height="14.1101pt" id="M613" style="vertical-align:-5.4742pt" version="1.1" viewbox="-0.0498162 -8.6359 14.0158 14.1101" width="14.0158pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.827,3.132)"><path d="M481 430L460 436C440 442 393 451 366 451C348 451 325 448 313 446C267 437 195 409 147 367C79 308 24 211 24 105C24 37 56 -12 93 -12C121 -12 156 1 199 32C246 66 313 122 349 168H351L286 -147C274 -205 261 -215 210 -224L199 -226L193 -255L438 -243L442 -214L417 -212C364 -208 359 -200 370 -140L433 204C455 324 469 389 481 430ZM391 385C382 336 366 260 358 238C321 178 209 59 143 59C129 59 115 83 115 131C115 207 152 317 220 373C243 392 282 403 314 403C348 403 374 395 391 385Z"></path></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/8728245/figures/8728245.fig.003b.svgz" name="8728245.fig.003b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Minimum spanning tree <svg height="9.01194pt" id="M614" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.96212 8.41168 9.01194" width="8.41168pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g></svg></td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/8728245/figures/8728245.fig.003c.svgz" name="8728245.fig.003c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Preorder traversal of <svg height="9.01194pt" id="M615" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.96212 8.41168 9.01194" width="8.41168pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g></svg></td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/8728245/figures/8728245.fig.003d.svgz" name="8728245.fig.003d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Approximate path</td></tr></table>

<div>An example of an approximate path.</div>

Complexity

fig3

Figure 3

Figure 3: Finding the Shortest Path with Vertex Constraint over Large Graphs 