An Application to Search for High-Priority War Opponent in Spatial Games Using Dynamic Skyline Query

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1 Intrntonl Journl o Appl Ennrn Rsr ISSN Volum 13, Numr 2 (218) pp An Applton to Sr or H-Prorty Wr Opponnt n Sptl Gms Usn Qury Jonwn Km Smt Lrl Arts Coll, Smyook Unvrsty, 815 Hwrn-ro, Nowon-u, Soul, 1795, Kor. E-ml:km@syu..kr ORCID: & Sopus Autor ID: Astrt. Wt t rnt vnmnts n loton-s srvs, mny onln n oln sptl ms v n vlop. In sptl ms, plyrs us rtn trrn turs or m mps o tul urn ms, survvl ms, or vrtul m sps n ply s tr r or lu plyrs n t m. T lu plyrs ompt nst r plyrs n n n wr ms wn runnn nto r plyrs. T lu plyrs n nrs tr os o wnnn t m ty n nty t lotons o nry r plyrs n t rsks ty pos n vn. In ts ppr, w propos n pplton or srn r plyrs wt low rsk to nrs t os o wnnn t m trou ynm skyln ury. A ynm skyln ury s n xtnson o t skyln ury, w s ury sm or multpl ttruts. Convntonl stus v monstrt t pplton o skyln urs n sptl ms; owvr, tr r rtn sortomns rrn t sr tm. Ts sortomns wr rsolv usn ynm skyln ury, n smulton sow tt su ury s st wn srn or surrounn r plyrs. Kywors: ury, Dynm skyln ury, Sptl m, Loton-s srvs, Su-ury INTRODUCTION Computr ms v vn rom n snl-plyr ms nto ntwork-s wr ms. Currntly, tr r mny multplyr ms wr multpl plyrs n prtpt n snl m smultnously. Wt mprovmnts n t mol nvronmnt n mp srvs, loton-s sptl ms v ppr n v n mnly us n wr ms su s Grs o Wr [1] n rstprson sootr (FPS) ms su s Ovrwt [2]. Sptl ms r ply y ntyn r n lu plyrs on mp. In prtulr, lu plyrs ompt nst r plyr n n n wr ms wn runnn nto r plyrs. I lu plyr otns normton on t surrounn r plyrs n vn, t n nlun t outom o t m. T os o wnnn sptl m nrss wn oosn sr opponnts y ntyn t lotons n rsks pos y opponnts, tt s, t m lvl. urs v n onut n sptl or mol ms to sr or opponnt mrs or s routs or nn nry loton wt os o wnnn t m [3]. T us o skyln ury to sr or t ots y omprn two or mor ttruts n ts s n stu. Howvr, t s urrntly us to ltr t n ntwork [4] or ts [5]. In sptl ms, t ury pont t t ntr o sr soul mov us plyr srs or otr plyrs n prtpts n wr ms wl movn. Ts stuy ppls ynm skyln ury to sr or opponnts y ntyn t surrounn r plyrs n sptl ms. Tt s, ts stuy ms to vry nw ppllty to mprov t os o wnnn ms y pplyn ynm skyln ury to t m r. Ts ppr ontruts to sptl ms n t ollown wys. It ukly srs or opponnts nr movn plyr n sptl ms. It trmns nry, low-rsk, n -prorty wr opponnts rom t surrounn opponnts. It srs t vlopmnt o nw pplton r or ynm skyln ury. BACKGROUND INFORMATION W stuy t pplton o ynm skyln urs to sr or nry low-rsk r plyrs n sptl m. Ts ston rly srs two sms: skyln ury n ynm skyln ury. Qury T skyln ury ws propos y Stpn Borzsony [6] n 21 to mprov t ury prormn o mult-ttrut t n ts. T sr or mult-ttrut t n ts uss su-urs wt SELECT sttmnts. T worst prormn s O(n^m) us t su-ury trts m srs or ttrut. A skyln ury smultnously trmns two or mor ttruts. For xmpl, t rtr or usr s prrr otl r t stn rom t n pr, tn t srs or p otl tt s los to t. In ts wy, skyln ury mprovs sr prormn y snntly run t numr o sr ots wn srn or ots vn two or mor ttruts. T nton o skyln ury s s ollows. Dnton: ury. I t ots p1 n p2 vn two-mnsonl ttruts r lmnts o tst P, n p1 p2 or two ttruts or p1 <p2 or t lst on ttrut, tn p1 omnts p2. Hr, t omnnt ot p1 s nlu n t skyln ury rsult. 1496

2 Pr($) Pr($) Intrntonl Journl o Appl Ennrn Rsr ISSN Volum 13, Numr 2 (218) pp As sr n t nton, ot s unr mor vorl ontons tn ot or ttrut, tn omnts. Bus t omnt t r rmov, t trt t or sr r ru s t numr o t ots n t omnt ron r rmov. A tl srpton o t skyln ury s s ollows. In nrl, t urnts r v nto our sps y rwn ross symol on ntr pont. T rst urnt s n uppr-rt sp n t ountrlokws urnt s t son urnt. Wn t sp s v nto our urnts s on, s sown n Fur 1, t ots (, ) n t rst urnt r omnt y us ty v lrr vlus tn n trms o stn n pr. Ts t r xlu rom t sr. Howvr, t ots n t son n ourt urnts r not ompltly omnt y wt two ttruts n soul r-vlut us ty v lrr or smllr vlu tn. For xmpl, n t ourt urnt s lrr stn ut lowr pr tn, n tus, t s not onsr to ompltly omnt y. Inst, s omnt y n ot s t omprson pros. Consuntly, t nl skyln ots r {,,, } Fur 1: ury n ots n tst Qury A ynm skyln ury n sr or p n nry otls s on t ns n poston o t usr n mol nvronmnt. Ts rs rom t stt ury pont o skyln ury. Tt s, ll ots n t son, tr, n ourt urnts soul mov to t rst urnt to vlut t surrounn ots [7]. For xmpl, t ury pont o usr movs to poston tt s 1 ml wy, s sown n Fur 3, t s not sy to rsonly trmn t ots (,,,,,, ) n trms o stn n pr. Ts s us t otvty o n vluton s low ompr to wn ll ots r n t sm urnt. Tror, ynm skyln ury xuts skyln ury tr movn t ots to t rst urnt o ury pont. Ts s on to rly ompr t ots n urnt s t ury pont movs. T rns twn skyln ury n ynm skyln ury or vlutn t surrounn ots o mr r nlyz n t nxt ston Fur 2: ury SEARCHING FOR SURROUNDING PLAYERS Ts ston provs n nlyss o t two skyln ury sms to sr or surrounn plyrs n sptl ms wl plyr s movn. It lso srs t vnts o ynm skyln ury y omprn skyln ury wt ynm skyln ury. Sptl Gm n Qury In sptl ms, srn or low-rsk plyrs rom surrounn plyrs wl movn rls ly on t sr tm ost. In ton, t sr or low-rsk n nry ots rom t urrnt poston rurs two omprson oprtons n monstrts omplxty. A skyln ury mprovs sr prormn y uln urnt s on t ury pont n lmntn ttruts wt vlus r tn tt o t ury pont rom t sr trts. T pross or trmnn t surrounn r plyrs wn usn skyln ury s sown n Fur 3. T skyln ury lwys uss 9 rn to t rt, nmly, t rst urnt, s t vluton r s on t orn. Tror, urnt soul sr n t ountrlokws rton to vlut ll surrounn ots. T skyln ots n urnt r {,,,,, }, s sown n Fur 3. Fur 4 sows skyln ury lortm. Frst, slt n rtrry ot o1 rom t t r rom sk n lult t ntr oornts (ln 1 4). Clult t oornts o t urnts s on t ntr oornts, n lmnt ll t o o1 n t rst urnt rom t sr trts (lns 5 n 6). I tr r no t omntn o1, tn o1 s rstr s skyln nt, n ll non-omnt ots r stor n nts_sky (lns 7 n 8). nt ots lso nlu ots o t son or ourt urnt tt nnot yt trmn s n omnt or not. Cnts r ompr n, n skyln ots r otn y storn ots tt r not ompltly omnt nto skyln_st (lns 1 14). 1497

3 Rsk lvl(%) Intrntonl Journl o Appl Ennrn Rsr ISSN Volum 13, Numr 2 (218) pp Pr($) Fur 3: ots rom rst to ourt urnts T skyln ury mntns low omplxty y snntly run t sr trts s on t omnnt rltonsp. Howvr, t lulton tm nrss us on mor vluton s onut y ntrtn skyln ots n urnt. Tl 1 summrzs t rns rom t ury pont or sr ots n t skyln ury. In ts wy, t nl trt soul slt y rvlutn t skyln ots o urnt s on t rsk n stn rom t loton o t plyr. Alortm-1: Qury Q-2.5 1: R t rom sk; 2: Do 3: Slt n o1 rnomly; 4: ntr.x <- o1.x; ntr.y <- o1.y; 5: Clults o 1, 2, 3, n 4-urnt.x n urrnt.y or ntyn t urnts; 6: Dlt ll t rom 1st urrnt o o1; 7: ny ots os not omnt o1; 8: nts_sky <- o1; 9: Loop 1: Do 11: Compr ll t n nts_sky; 12: tr r no ots otr n omnn rltonsp; 13: skyln_st <- o1; 14: Loop Fur 4: ury lortm Tl 1 sows t solut vlus o t rns twn ury pont n ot. Altou t skyln ots r sr n urnt, t omnnt rltonsp must trmn s on t movn rton o ot. Tror, omprson oprtons twn t skyln ots r rur. T skyln ots tr rlulton s on t solut vlu r {,, }. T rst n son urnts ontn ots or skyln ury, ut tr r no ots n t tr or ourt urnts. Ts s us,, n r omnt y n t rlton,, n. As rsult, t ots o urnt mt not nlu us t solut vlu s vlut s on t rn rom. Sptl Sr o Qury To vlut ll ots, t ynm skyln ury movs t surrounn ots to t rst urnt s on t rton towr w t ury pont movs. Ts solvs t ly Movn Q-1 Q-3 Q-4 prolm tt ours wn t skyln ury ollts n rvluts t skyln ots tr rst vlutn t ots n urnt. In ts wy, opponnts n sptl ms n ukly vlut us ty r s on t movn poston o t plyr. Tl 1: ots n urnt n tr rns rom ury pont Qurnts Ots ABS. rom (1,7) 1 (1.3, 8) (.3, 1) 2 (.9, 4), (.8, 1) (.1, 7), (.2, 3) 3 (.5, 4) (.5, 3) 4 (1.5, 3), (2, 55) (.5, 4), (1, 15) In ynm skyln ury, ll ots n urnt r mov to t rst urnt, llown plyr to sr or opponnt mrs wl movn, s sown n Fur 5. T mov ots r vlut n t rst urnt, n t skyln ots r {,,, } Fur 5: Movn ots to t rst urnt n ynm skyln ury T rn twn t ynm skyln ury n t skyln ury lortm, sown n Furs 6 n 3, s movn t ots n urnt to t rst urnt. All ots r mov to t rst urnt, n ust lk wt t skyln ury, ots r sr s on ury pont. Alortm-2: Qury 1: R t rom sk; 2: = 2; 3: Do 4: Mov ots n Q- to Q-1; 5: ++; 6: Loop 7:... //Sm os wt Alortm-1 Fur 6: Dynm skyln ury lortm PERFORMANCE EVALUATION Ts ston srs smulton o t skyln n ynm skyln urs n ppls t to sptl ms. 1498

4 Intrntonl Journl o Appl Ennrn Rsr ISSN Volum 13, Numr 2 (218) pp k Smulton Envronmnts W rt 1 K vrtul ots usn sptl t nrtor [8] tt ontns t loton o t mrs. A unorm struton n Gussn struton r us to msur t prormn o t vrtul t orn to t struton o t t, s sown n Fur 7. 8.k y 6.k 4.k 2.k T smulton nvronmnts r s ollows. T sptl ots us r t rl n syntt t. T rl t wr otn rom uln lotons n Kor n syntt t wr nrt y tool. T struton o rl t s not unorm; owvr, t syntt t ollow unorm n Gussn strutons. T sptl ots r mn wt R-tr us ty v two-mnsonl t o loton... 2.k 4.k 6.k 8.k 1.k 8.k 1.k x () Unorm 1.k 8.k Tl 2: Smulton nvronmnts n t summry Rl Dt Syntt Dt 65,536 1, Dstruton Skw Unorm, Gussn 6.k y Ctory Sptl ots 4.k Inx Ron R-tr (wt rsky lvl ttruts) Soul, Kor 2.k Vrtul sp Dv. Lnu C++ Sms Qury, Dynm Qury Systm Lnux (For), RAM 8 GB, Intl Xon 3.2 GHz.. 2.k 4.k 6.k x () Gussn Fur 7: Syntt tst nrt y sptl t nrtor n unorm n Gussn strutons Tl 3 sows t ontons or nrtn Gussn struton t. T sptl ots r nrt y sttn t ntr sp to 1 K. T mn n sm r st to 5 n 3 K, rsptvly. T tst nrt s twomnsonl sptl t, us t mrs r lot on mp or wtn orp sp n m. T sp sz s vrtul sp. In Tl 3, oxs r sptl ots, n t sz s rnomly nrt s on 19,372 ss. 46.k 458.k 456.k Lttu 454.k Tl 3: Dt nrton ontons or Gussn struton 452.k 45.k 448.k Worl Sttns: Dmnsons [1..3]: 2 Sz [1..1, 1..1]: 1, 1 Gnrtor Sttns: Boxs rt [1..1]: 1 H rns or t ox sz [ , ]: 2, 3 Vrl sz o oxs: Ys Non-zro sz o oxs: Ys Dstruton: Guss (Mn: 5., Sm: 3.) S [ ]: k 194.k 196.k 198.k 2.k 22.k 24.k Lontu Fur 8: Sptl t o ulns n Soul, Kor Fur 9 sows t msur tm tkn to sr or skyln ots n unormly strut tst o syntt t. A ynm skyln ury sows str prossn tm tn skyln ury, s sown n Fur 9. A skyln ury rurs lonr sr tm tn ynm skyln ury us t xuts skyln ury n urnt wn srn or ots, n tn xuts skyln ury on mor tm. T pont t w t sr tm ns to nrs s 8 K. R-tr [9] nxs r us or sptl ots, n no s ust to nlu t rsk. Ts smulton us uln t n Soul [1] to ompr t prormn wn usn rl sptl t (Fur 8). T tst us n t xprmnt s v nto 2 K unts. T sr tm nots t vr vlus prorm 1 tms or unt. Hr, t omponnts o t t r n y omposn 1 roups o 2 K t rntly tm. Fur 1 sows t sr tm o skyln ots n Gussn struton. Tr s no rn n t sr tm up to t ntl 2 K. Howvr, t tks lonr s t mount o t nrss. Tt s, Gussn struton sows prormn rton o pproxmtly.23 n.25 or skyln ury n ynm skyln ury, rsptvly, ompr wt unorm struton. Ts rlts tt t t r onntrt n Gussn Sr Prormn o s T sr prormn must vlut to nsur t sp o t m n ompr t rsults twn skyln ury n ynm skyln ury. 1499

5 Sr tm(ms) Sr tm(ms) Sr tm(ms) Intrntonl Journl o Appl Ennrn Rsr ISSN Volum 13, Numr 2 (218) pp struton. Howvr, skyln ury tks mor tm tn ynm skyln ury us t srs or skyln ots n urnt n tn r-lults tm or ll o t urnts Fur 9: Sr tm or unorm struton A sr usn rl t sows str sr tm ompr to usn t vrtul xprmntl t, s sown n Fur 11. Ts rlts t sprsly strut ulns n Soul, s sown n Fur 8. T xprmnt sow tt ynm skyln rsults n str sr prormn tn t xstn skyln or ot vrtul n rl t. A skyln ury nluns t sr sp us t rst otns t skyln ots n urnt n rlults ll o tm n. Contrry to ts, ynm skyln s rltvly st us t movs sptl ots to t rst urnt, n tn srs or t skyln ots n snl oprton. Altou t tks tm or ynm skyln to mov t ots rom t son, tr, n ourt urnts to t rst urnt, ts s lttl t on t ovrll sr prormn K 4K 6K 8K 1K Dt ots 2K 4K 6K 8K 1K Dt ots Fur 1: Sr tm or Gussn struton CONCLUSION T ynm skyln ury ppl n ts stuy sow str sr tn skyln ury wn srn or surrounn mrs. Ts lps nrs t os o wnnn m y ukly ntyn low-rsk opponnts tt r nry. In prtulr, ynm skyln ury n sr or surrounn mrs mor omprnsvly tn skyln ury, tus run t sr tm n vn ury sr or skyln ots. Ts stuy prov t slty o nw typ o m sr y pplyn t skyln mto, w s sr sm or t wt multpl ttruts n m r. In utur, w wll nlyz n vlut mor vn sr mtos y xpnn vrous typs o skyln urs nto rnt ms K 3K 4K 5K 6K Dt ots Fur 11: Sr tm or rl tst ACKNOWLEDGEMENTS Ts work ws support y t Ntonl Rsr Founton o Kor Grnt un y t Korn Govrnmnt [NRF-217R1D1A1B335884] n ts work ws lso support y t Austrln Govrnmnt, t Dprtmnt o Euton, Employmnt n Workpl Rltons (now Dprtmnt o Euton n Trnn) unr t 211 Envour Awrs. REFERENCES [1] Grs o wr: ttps://rsowr.om [2] Ovrwt: ttps://plyovrwt.om [3] Jonwn K. n Duksn O. (215). Trtn nms usn rvrs skyln ury n sptl m. Intrntonl Journl o Appl Ennrn Rsr. v. 1(1), pp [4] Hkn C., Sun Z., n Jon G. (27). Towrs nry-nt skyln montorn n wrlss snsor ntworks. EWSN, LNCS 4373, pp [5] Yon J. R., Inul S., Joo H. J., Kyoun G. W., n Myoun H. K. (213). Enry-nt twomnsonl skyln ury prossn n wrlss snsor ntworks. 1t Annul IEEE-CCNC Smrt Sps n Snsor Ntworks, pp [6] Stpn B., Donl K., n Konr S. (21). T skyln oprtor. ICDE, pp [7] ZBn Y., XoNu Y., n Xu Z. (215). Unrtn ynm skyln urs or unrtn tss. Intrntonl Conrn on Fuzzy Systms n Knowl Dsovry (FSKD), Zn Au., 215, pp [8] Sptl t nrtor. DVsul Co1.. [9] Guttmn, A. (1984). R-Trs: A ynm nx strutur or sptl srn, Prons o ACM mnmnt o t (SIGMOD), Boston, Jun, 1984, pp [1] Buln loton normton o Soul, Kor (216). ttp://t.soul.o.kr 15