Subgraph-Indexed Sequential Subdivision for Continuous Subgraph Matching on Dynamic Knowledge Graph

<table class="algorithm-group"><tr><td><table class="algorithm" id="alg3"><tr><td>(1)</td><td><b>repeat</b></td></tr><tr><td colspan="2">(2) Apply State Transition Rules 1–6</td></tr><tr><td>(3)</td><td><b>until</b> No Candidate Transition in <i>FG;</i></td></tr><tr><td>(4)</td><td><b>Return</b><svg height="9.69047pt" id="M713" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -9.34054 10.8779 9.69047" width="10.8779pt" 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="M799 12L418 655H408L27 12L34 0H792L799 12ZM711 50H115L413 553L711 50Z"></path></g></svg><i>FG</i><svg height="8.8423pt" id="M714" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 3.66193 8.8423" width="3.66193pt" 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="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z"></path></g></svg></td></tr></table></td></tr></table>

<div> IncMaintenance (<i>FG</i>, <span class="nowrap"><svg height="12.6316pt" id="M712" style="vertical-align:-3.29106pt" version="1.1" viewbox="-0.0498162 -9.34054 22.7937 12.6316" width="22.7937pt" 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="M799 12L418 655H408L27 12L34 0H792L799 12ZM711 50H115L413 553L711 50Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.778,0)"><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,-0.0091,19.605,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g></svg>).</span></div>

Complexity

alg3

Algorithm 3

Algorithm 3: Subgraph-Indexed Sequential Subdivision for Continuous Subgraph Matching on Dynamic Knowledge Graph 