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(on) ] TJ 0 -10.959 TD [ (dynamic) -355.003 (graphs\056) -356.999 (Our) -355.003 (pr) 8.008 (op) -7.004 (ose) -7.004 (d) -354.992 (appr) 7.997 (oach) -355.996 (is) -355.003 (base) -7.004 (d) -355.996 (on) -355.003 (the) -355.003 (state\055) ] TJ 0 -10.959 TD [ (of\055the\055art) -254.004 (2\055hop) -254.996 (inde) 7.004 (x) -254.004 (for) -254.004 (LCR) -254.996 (queries\056) -254.004 (In) -253.993 (this) -255.008 (pap) -6.993 (er) 57.994 (\054) -253.993 (w) 7.997 (e) -254.996 (pr) 7.997 (esent) ] TJ 0.982 0 0 1 53.798 435.879 Tm [ (e\034cient) -253 (algorithms) -254.004 (for) -253 (up) -6.993 (dating) -254.004 (the) -253 (inde) 7.004 (x) -253 (structur) 7.997 (e) -254.004 (in) -253 (r) 8.008 (esp) -7.004 (onse) -253 (to) ] TJ 0.98 0 0 1 53.798 424.92 Tm [ (dynamic) -224.003 (e) -6.993 (dge) -223.01 (insertions\057deletions) -223.992 (and) -224.003 (demonstrate) -222.999 (the) -224.003 (corr) 8.008 (e) -7.004 (ctness) ] TJ 0.982 0 0 1 53.798 413.961 Tm [ (of) -254.004 (our) -253.993 (up) -7.004 (date) -254.004 (algorithms\056) -253.993 (Follo) 6.993 (wing) -253.993 (that\054) -254.004 (w) 7.997 (e) -253.993 (pr) 9 (esent) -254.004 (that) -254.004 (adopting) ] TJ 1.02 0 0 1 53.798 403.003 Tm [ (a) -299.998 (quer) -15 (y\055friendly) -299.005 (but) -299.998 (up) -7.004 (date\055unfriendly) -299.998 (inde) 7.004 (xing) -299.998 (scheme) -300.009 (r) 8.008 (esults) ] TJ T* [ (in) -299.998 (surprisingly) -299.005 (sup) -6.993 (erb) -300.009 (quer) -13.997 (y\057up) -7.004 (date) -299.998 (e\034ciency) -298.994 (and) -300.009 (outp) -6.993 (erforms) ] TJ 1.008 0 0 1 53.798 381.085 Tm [ (those) -248.996 (up) -7.004 (date\055friendly) -248.996 (ones\056) -249.007 (W) 79.999 (e) -248.996 (analyze) -248.996 (and) -249.007 (demonstrate) -248.996 (that) -248.996 (t) 0.993 (h) -0.993 (e) ] TJ 1.02 0 0 1 53.798 370.126 Tm [ (quer) -15 (y\055friendly) -259 (inde) 6 (xing) -259 (scheme) -260.004 (actually) -259 (achie) 6 (v) 8.008 (es) -259 (the) -260.004 (same) -260.004 (time) ] TJ 0 -10.959 TD [ (comple) 7.004 (xity) -282.008 (as) -280.993 (those) -281.997 (of) -282.008 (up) -6.993 (date\055friendly) -281.005 (ones\056) -281.997 (Finally) 57.994 (\054) -281.997 (w) 7.997 (e) -281.997 (pr) 7.997 (esent) ] TJ 0 -10.959 TD [ (the) -352.996 (batche) -7.004 (d) -352.996 (up) -7.004 (d) 1.004 (ate) -353.007 (algorithms) -352.996 (wher) 7.997 (e) -352.996 (the) -353.007 (up) -6.993 (dates) -353.007 (may) -352.996 (include) ] TJ 0 -10.959 TD [ (multiple) -313.994 (e) -7.004 (dge) -313.002 (insertions\057deletions\056) -313.994 (Extensiv) 6.993 (e) -313.002 (e) 7.004 (xp) -7.004 (eriments) -313.994 (sho) 6.993 (w) ] TJ 0.98 0 0 1 53.798 326.29 Tm [ (the) -233.003 (e\035e) -6.993 (ctiv) 7.997 (eness) -231.999 (of) -233.003 (the) -231.999 (pr) 7.997 (op) -6.993 (ose) -7.004 (d) -233.003 (up) -6.993 (date) -233.003 (algorithms\054) -231.999 (quer) -16.004 (y\055friend) 1.004 (ly) ] TJ 1 0 0 1 53.798 315.331 Tm [ (inde) 7.004 (xing) -250 (scheme) 9.993 (\054) -250 (and) -250 (batche) -6.993 (d) -250 (up) -7.004 (date) -250 (algorithms\056) ] TJ /T1_3 7.97 Tf 0 -20.122 TD [ (P) -24.002 (VLDB) -249.997 (Refer) 8.005 (ence) -250.01 (Format\072) ] TJ /T1_1 7.97 Tf -0.263 -9.962 Td [ (Xin) -249.997 (Chen\054) -250.01 (Y) 71.003 (ou) -249.997 (Peng\054) -249.997 (Sib) -10 (o) -249.997 (W) 59.999 (ang\054) -250.01 (and) -249.997 (Je\035r) 8.005 (e) 7.001 (y) -250.01 (Xu) -249.997 (Y) 39.008 (u\056) -250.01 (DLCR) -249.997 (\072) -249.997 (E\034cient) ] TJ 0.263 -9.963 Td [ (Inde) 7.001 (xing) -249.997 (for) -250.01 (Lab) -10 (el\055Constraine) -7.001 (d) -249.997 (Reachability) -249.997 (Queries) -249.997 (on) -249.997 (Large) -250.01 (D) -10 (ynamic) ] TJ 0 -9.963 TD [ (Graphs\056) -249.997 (P) -24.002 (VLDB\054) -249.997 (15\0508\051\072) -250.01 (1645\0551657\054) -249.997 (2022\056) ] TJ 0 -10.958 TD (doi\07210\05614778\0573529337\0563529348) Tj /T1_3 7.97 Tf 0 -18.467 TD [ (P) -24.002 (VLDB) -249.997 (Artifact) -249.997 (A) 64.993 (vailability\072) ] TJ /T1_1 7.97 Tf 1.017 0 0 1 53.559 224.937 Tm [ (The) -245.995 (sour) 6.989 (ce) -245.995 (co) -7.001 (de) 10 (\054) -245.995 (data\054) -246.998 (and\057or) -246.007 (other) -245.995 (artifacts) -246.998 (hav) 7.992 (e) -245.995 (b) -10 (e) -7.001 (en) -246.007 (made) -246.998 (available) -245.995 (at) ] TJ 1 0 0 1 53.798 213.978 Tm [ (https\072\057\057github) 20 (\056com\057jer) 8.005 (chenxin\057DP2H\055) -63.011 (CUHK\056) ] TJ /T1_3 10.909 Tf 0 -21.817 TD [ (1) -1000 (IN) -36.997 (TRODUCTION) ] TJ /T1_1 8.966 Tf 1.02 0 0 1 53.798 178.463 Tm [ (Graph) -245.996 (is) -247 (a) -246.007 (fundamental) -245.996 (data) -247 (structur) 7.997 (e) -245.996 (that) -245.996 (captur) 6.993 (es) -245.996 (complicate) -7.004 (d) ] TJ 0.997 0 0 1 53.798 167.504 Tm [ (conne) -7.004 (ctions) -251.996 (b) -10.004 (etw) 8.008 (e) -7.004 (en) -251.996 (entities\056) -252.007 (Many) -251.996 (r) 7.997 (eal\055w) 8.008 (orld) -252.007 (graphs\054) -251.996 (e) 10.004 (\056g\056\054) -252.007 (so) -6.993 (cial) ] TJ ET q 1 0 0 1 53.798 157.649 cm 0.398 w 0 0 m 47.821 0 l S Q BT /T1_2 5.479 Tf 53.798 151.487 Td (\052) Tj /T1_1 6.974 Tf 2.367 -2.64 Td [ (Y) 70.994 (ou) -249.993 (Peng) -250.007 (is) -249.993 (the) -250.007 (corr) 8.001 (esp) -6.998 (onding) -249.993 (author) -250.007 (and) -249.993 (joint) -250.007 (\033rst) -249.993 (author) 58.992 (\056) ] TJ -1.869 -8.404 Td [ (This) -250.007 (w) 8.001 (ork) -249.993 (is) -250.007 (license) -6.998 (d) -249.993 (under) -250.007 (the) -249.993 (Cr) 8.001 (eativ) 7.987 (e) -249.993 (Commons) -250.007 (BY) 49.012 (\055NC\055ND) -250.007 (4\0560) -249.993 (International) ] TJ -0.498 -7.97 Td [ (License) 9.995 (\056) -249.993 (Visit) -250.007 (https\072\057\057cr) 8.001 (eativ) 8.001 (e) -6.998 (commons\056org\057licenses\057by\055) -70.994 (nc\055) -72.012 (nd\0574\0560\057) -249.993 (to) -250.007 (vie) 7.012 (w) -250.007 (a) -249.993 (cop) 6.998 (y) -250.007 (of) ] TJ 0 -7.97 TD [ (this) -250.007 (license) 10.009 (\056) -250.007 (For) -249.993 (any) -250.007 (use) -249.993 (b) -10.009 (e) 7.012 (y) 8.001 (ond) -250.007 (those) -249.993 (co) 6.998 (v) 8.001 (er) 7.987 (e) -6.998 (d) -249.993 (by) -250.007 (this) -249.993 (license) 9.995 (\054) -249.993 (obtain) -250.007 (p) -6.998 (ermission) -249.993 (by) ] TJ 0.995 0 0 1 53.798 116.533 Tm [ (emailing) -250.007 (info\100) -9.995 (vldb) 20.003 (\056org\056) -250.007 (Cop) 6.998 (yright) -249.993 (is) -250.007 (held) -248.989 (by) -250.007 (the) -249.993 (o) 6.998 (wner\057author\050) 12.002 (s\051\056) -250.007 (Publication) -249.993 (rights) ] TJ 1 0 0 1 53.798 108.563 Tm [ (license) -6.998 (d) -250.007 (to) -249.993 (the) -250.007 (VLDB) -249.993 (Endo) 6.998 (wment\056) ] TJ T* [ (Pr) 8.001 (o) -6.998 (ce) -6.998 (e) -7.012 (dings) -249.993 (of) -250.007 (the) -249.993 (VLDB) -250.007 (Endo) 7.012 (wment\054) -250.007 (V) 79.999 (ol\056) -249.993 (15\054) -250.007 (No) 10.009 (\056) -250.007 (8) -250.007 (ISSN) -249.993 (2150\0558097\056) ] TJ T* (doi\07210\05614778\0573529337\0563529348) Tj /T1_1 8.966 Tf 1.02 0 0 1 317.955 592.044 Tm [ (netw) 7.997 (orks\054) -272.997 (biological) -272.997 (netw) 7.997 (orks\054) -272.997 (and) -273.008 (kno) 6 (wle) -6 (dge) -272.997 (graphs\054) -272.997 (ar) 7.004 (e) -273.008 (e) -6 (dge\055) ] TJ 0 -10.959 TD [ (lab) -10.004 (ele) -6.993 (d\054) -275.004 (wher) 7.997 (e) -274.993 (each) -275.004 (e) -6.993 (dge) -274.001 (is) -275.004 (asso) -7.004 (ciate) -6.993 (d) -275.004 (with) -275.004 (a) -274.993 (lab) -10.004 (el) -274.993 (and) -275.004 (di\035er) 7.997 (ent) ] TJ 1.019 0 0 1 317.955 570.126 Tm [ (lab) -10.004 (els) -244 (indicate) -244.992 (di\035er) 7.997 (ent) -244 (r) 7.997 (elationships\056) -244.992 (For) -244 (instance) 9.993 (\054) -245.004 (on) -244 (so) -6.993 (cial) -244 (net\055) ] TJ 0.992 0 0 1 317.623 559.167 Tm [ (w) 7.997 (orks\054) -251.996 (the) -251.004 (r) 8.008 (elationships) -252.007 (b) -9.993 (etw) 7.997 (e) -7.004 (en) -250.993 (tw) 7.997 (o) -251.996 (users) -251.004 (could) -251.996 (take) -252.007 (in) -250.993 (a) -252.007 (variety) ] TJ 0.98 0 0 1 317.955 548.208 Tm [ (of) -198.006 (forms\054) -196.991 (e) 9.993 (\056g\056\054) -197.995 <10466f6c6c6f> 6.993 <7711> 50.009 (\054) -197.002 <104c696b65> 24.001 <11> 49.998 (\054) -197.002 (and) -197.995 <10667269656e644f66> -73.998 <11> 49.998 (\056) -198.006 (On) -197.995 (such) -197.002 (e) -7.997 (dge\055lab) -10.004 (ele) -7.004 (d) ] TJ 0.992 0 0 1 317.955 537.249 Tm [ (graphs\054) -251.004 (a) -250.993 (fundamental) -251.004 (typ) -7.004 (e) -250.993 (of) -250 (graph) -251.004 (quer) -15 (y) -251.004 (is) -250.993 (the) ] TJ /T1_4 8.966 Tf 181.32 0 Td [ (lab) -10.004 (el\055constraine) -6.993 (d) ] TJ 0.98 0 0 1 317.955 526.29 Tm [ (r) 7.997 (eachability) -228.999 (\050LCR\051) ] TJ /T1_1 8.966 Tf 67.284 0 Td [ (quer) -15 (y) 60.002 (\056) -230.003 (In) -228.999 (an) -230.003 (LCR) -229.992 (quer) -15 (y) 59.991 (\054) -228.988 (it) -230.003 (takes) -228.999 (as) -230.003 (input) -230.003 (a) -228.999 (sour) 7.997 (ce) ] TJ -67.284 -10.959 Td [ (no) -7.004 (de) ] TJ /T1_5 8.966 Tf 1 0 0 1 336.881 515.331 Tm (B) Tj /T1_1 8.966 Tf 0.98 0 0 1 340.678 515.331 Tm [ (\054) -189.006 (a) -187.991 (target) -189.006 (no) -7.004 (de) ] TJ /T1_5 8.966 Tf 1 0 0 1 391.727 515.331 Tm (C) Tj /T1_1 8.966 Tf 0.98 0 0 1 395.331 515.331 Tm [ (\054) -189.006 (and) -187.991 (a) -189.006 (lab) -9.993 (el) -188.002 (set) ] TJ /T1_6 8.966 Tf 1 0 0 1 450.058 515.331 Tm <09> Tj /T1_1 8.966 Tf 0.98 0 0 1 456.28 515.331 Tm [ (\056) -189.006 (The) -187.991 (quer) -16.004 (y) -188.002 (then) -188.994 (r) 7.997 (eturns) -188.002 (true) ] TJ -141.148 -10.959 Td [ (if) -239.003 (ther) 9 (e) -238.992 (e) 6.993 (xists) -238 (a) -239.003 (path) ] TJ /T1_5 8.966 Tf 1 0 0 1 392.24 504.372 Tm (\045) Tj /T1_1 8.966 Tf 0.98 0 0 1 399.657 504.372 Tm [ (fr) 7.997 (om) ] TJ /T1_5 8.966 Tf 1 0 0 1 418.686 504.372 Tm (B) Tj /T1_1 8.966 Tf 0.98 0 0 1 424.579 504.372 Tm (to) Tj /T1_5 8.966 Tf 1 0 0 1 433.566 504.372 Tm (C) Tj /T1_1 8.966 Tf 0.98 0 0 1 439.266 504.372 Tm [ (such) -239.003 (that) -238 (the) -238.992 (la) 0.993 (b) -10.997 (el) ] TJ /T1_5 8.966 Tf 1 0 0 1 506.829 504.372 Tm (\137) Tj /T1_1 8.966 Tf 0.98 0 0 1 513.668 504.372 Tm [ (of) -238 (each) -239.003 (e) -6.993 (dge) ] TJ /T1_5 8.966 Tf 1 0 0 1 317.641 493.413 Tm (4) Tj /T1_1 8.966 Tf 1.02 0 0 1 324.257 493.413 Tm [ (on) -260.997 (path) ] TJ /T1_5 8.966 Tf 1 0 0 1 355.202 493.413 Tm (\045) Tj /T1_1 8.966 Tf 1.02 0 0 1 362.911 493.413 Tm [ (b) -10.004 (elongs) -260.997 (to) ] TJ /T1_6 8.966 Tf 1 0 0 1 404.128 493.413 Tm <09> Tj /T1_1 8.966 Tf 1.02 0 0 1 410.351 493.413 Tm [ (\054) -260.997 (and) -261.008 (other) -15 (wise) -260.997 (r) 7.997 (eturns) -260.997 (false) 10.004 (\056) ] TJ 0 0 0 rg 108.655 0 Td [ (A) 12 (s) -260.997 (sho) 6.993 (wn) ] TJ -199.239 -10.958 Td [ (in) -295.001 (\133) ] TJ 1 0 0 1 331.344 482.455 Tm (13) Tj 1.02 0 0 1 339.683 482.455 Tm (\054) Tj 1 0 0 1 344.393 482.455 Tm (20) Tj 1.02 0 0 1 352.732 482.455 Tm <15> Tj 1 0 0 1 357.744 482.455 Tm (22) Tj 1.02 0 0 1 366.082 482.455 Tm (\054) Tj 1 0 0 1 370.792 482.455 Tm (28) Tj 1.02 0 0 1 379.131 482.455 Tm [ (\135\054) -295.001 (LCR) -295.001 (queries) -295.001 (\033nd) -295.001 (many) -294.99 (applications) -295.001 (on) -295.001 (so) -7.004 (cial) ] TJ 0.98 0 0 1 317.955 471.496 Tm [ (netw) 7.997 (orks\054) -224.996 (biological) -224.003 (netw) 7.997 (orks\054) -224.996 (kno) 7.004 (wle) -7.004 (dge) -224.996 (graphs\054) -225.007 (etc\056) -224.996 (For) -224.003 (instance) 10.004 (\054) ] TJ 0.982 0 0 1 317.955 460.537 Tm [ (on) -254.996 (a) -254.004 (so) -7.004 (cial) -254.996 (netw) 7.997 (ork\054) -253.993 (an) -255.008 (LCR) -254.996 (quer) -15 (y) -254.004 (can) -254.996 (b) -9.993 (e) -255.008 (use) -7.004 (d) -254.996 (to) -254.004 (determine) -254.996 (if) -253.993 (tw) 7.997 (o) ] TJ 1.001 0 0 1 317.731 449.578 Tm [ (v) 7.997 (ertices) -248.996 (ar) 7.997 (e) -248.996 (r) 7.997 (elate) -6.993 (d) -248.004 (via) -248.996 (a) -249.007 (series) -248.996 (of) -248.996 (giv) 7.997 (en) -248.996 (r) 7.997 (elationships\056) -248.004 (Another) -248.996 (e) 6.993 (x\055) ] TJ 0.983 0 0 1 317.955 438.619 Tm [ (ample) -254.996 (of) -256 (application) -255.008 (is) -254.996 (on) -254.996 (kno) 6.993 (wle) -6.993 (dge) -256 (graphs\056) -255.008 (Regular) -254.996 (path) -256 (queries) ] TJ 0.98 0 0 1 317.955 427.66 Tm [ (hav) 7.997 (e) -245.996 (b) -10.997 (e) -7.004 (en) -245.996 (e) 6.993 (xtensiv) 8.008 (ely) -247 (e) 6.993 (xplor) 9 (e) -7.997 (d) -245.996 (on) -247 (kno) 6.993 (wle) -6.993 (dge) -246.007 (graphs) -247 (\133) ] TJ 1 0 0 1 514.804 427.66 Tm (3) Tj 0.98 0 0 1 518.973 427.66 Tm (\054) Tj 1 0 0 1 523.073 427.66 Tm (4) Tj 0.98 0 0 1 527.243 427.66 Tm (\054) Tj 1 0 0 1 531.343 427.66 Tm (31) Tj 0.98 0 0 1 539.682 427.66 Tm [ (\135) -247 (and) ] TJ 0.984 0 0 1 317.955 416.701 Tm [ (ar) 7.997 (e) -253 (supp) -6.993 (orte) -8.008 (d) -253 (by) -253 (practical) -253.993 (graph) -253 (quer) -15 (y) -254.004 (languages) -253 (such) -254.004 (as) -253 (SP) 60.002 (ARQL) ] TJ 1.02 0 0 1 317.749 405.742 Tm [ (1\0561\054) -262 (PGQL) -262 (\133) ] TJ 1 0 0 1 360.786 405.742 Tm (27) Tj 1.02 0 0 1 369.125 405.742 Tm [ (\135\054) -262 (and) -262 (op) -7.004 (enCypher\133) ] TJ 1 0 0 1 442.443 405.742 Tm (11) Tj 1.02 0 0 1 450.781 405.742 Tm [ (\135\056) -262 (LCR) -262 (queries) -262 (ar) 7.997 (e) -262 (one) -262 (of) -260.997 (the) ] TJ 1 0 0 1 317.955 394.783 Tm [ (most) -250 (imp) -7.004 (ortant) -250 (op) -6.993 (erators) -250 (in) -250 (r) 7.997 (egular) -250 (path) -250 (queries\056) ] TJ 0 g 0.98 0 0 1 327.918 383.824 Tm [ (In) -235 (the) -235 (ab) -10.004 (o) 7.004 (v) 7.997 (e) -235 (applications\054) -235 (graphs) -235 (ar) 7.997 (e) -235 (usually) -235 (dynamically) -235.992 (chang\055) ] TJ -10.166 -10.958 Td [ (ing\056) -194.002 (For) -194.002 (e) 8.008 (xample) 9.993 (\054) -194.002 (on) -192.998 (so) -7.997 (cial) -192.998 (netw) 7.997 (orks\054) -194.002 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(d) ] TJ 1.02 0 0 1 317.955 329.03 Tm [ (by) -274.001 (Peng) -272.997 (et) -274.001 (al\056) -274.001 (is) -272.997 (base) -7.004 (d) -274.001 (on) -274.001 (the) -272.997 (2\055hop) -274.001 (inde) 7.004 (x\054) -274.001 (and) -273.008 (assumes) -274.001 (that) -274.001 (the) ] TJ 0.98 0 0 1 317.955 318.071 Tm [ (input) -245.996 (graph) -247 (is) -246.007 (static\056) -247 (When) -245.996 (the) -245.996 (graph) -247 (has) -246.007 (change) -6.993 (d\054) -247 (the) -246.007 (P2H\053) -247 (inde) 8.008 (x) ] TJ 1.02 0 0 1 317.955 307.112 Tm [ (no) -290.997 (longer) -290.997 (w) 6.993 (orks\056) -290.997 (Computing) -290.997 (the) -291.009 (P2H\053) -291.99 (inde) 6.993 (x) -290.997 (fr) 7.997 (om) -290.997 (scratch) -290.997 (after) ] TJ T* [ (e) 7.004 (v) 7.997 (er) -15 (y) -283.001 (up) -7.004 (date) -281.997 (is) -283.001 (not) -283.001 (a) -281.997 (sound) -283.001 (option) -283.001 (since) -281.997 (the) -283.001 (inde) 7.004 (x) -283.001 (construction) ] TJ 0 -10.959 TD [ (still) 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