MinCounter: An Efficient Cuckoo Hashing Scheme for Cloud Storage Systems

Transcription

1 MinCounter: An Effiient Cukoo Hshing Sheme for Cloud Storge Systems Yunyun Sun Yu Hu Dn Feng Ling Yng Pengfei Zuo Shunde Co Wuhn Ntionl L for Optoeletronis, Shool of Computer Huzhong University of Siene nd Tehnology, Wuhn, Chin {sunyunyun, syhu, dfeng, yling, pfzuo, sd}@hust.edu.n Corresponding Author: Yu Hu (syhu@hust.edu.n) Astrt With the rpid growth of the mount of informtion, loud omputing servers need to proess nd nlyze lrge mounts of high-dimensionl nd unstrutured dt timely nd urtely, whih usully requires mny query opertions. Due to simpliity nd ese of use, ukoo hshing shemes hve een widely used in rel-world loud-relted pplitions. However, due to the potentil hsh ollisions, the ukoo hshing suffers from endless loops nd high insertion lteny, even high risks of re-onstrution of entire hsh tle. In order to ddress this prolem, we propose ost-effiient ukoo hshing sheme, lled MinCounter. The ide ehind MinCounter is to llevite the ourrene of endless loops in the dt insertion. MinCounter selets the old (infrequently essed) ukets to hndle hsh ollisions rther thn rndom ukets. MinCounter hs the slient fetures of offering effiient insertion nd query servies nd otining performne improvements in loud servers, s well s enhning the eperienes for loud users. We hve implemented MinCounter in lrge-sle loud tested nd emined the performne y using two rel-world tres. Etensive eperimentl results demonstrte the effiy nd effiieny of MinCounter. I. INTRODUCTION In the er of Big Dt, loud omputing servers need to proess nd nlyze lrge mounts of dt timely nd urtely. Aording to the report of Interntionl Dt Corportion(IDC) in 14, the dt we rete nd opy nnully will reh 44 ZettBytes in [1]. Lrge frtions of mssive dt ome from the populr use of moile devies [1]. Due to the onstrined energy nd limited storge pity, rel-time proessing nd nlysis re nontrivil in the ontet of loud-sed pplitions. In order to support rel-time queries, hshing-sed dt strutures hve een widely used in onstruting the inde due to onstnt-sle ddressing ompleity nd thus fst query response. Unfortuntely, hshing-sed dt strutures use low spe utiliztion, s well s high-lteny risk of hndling hshing ollisions. Unlike onventionl hsh tles, ukoo hshing [2] ddresses hshing ollisions vi simple kikingout opertion (i.e., flt ddressing), rther thn serhing the linked lists (i.e., hierrhil ddressing). The ukoo hshing mkes use of d 2 hsh tles, nd eh item hs d ukets for storge. Cukoo hshing selets suitle uket for inserting /15/$ IEEE new item nd llevites hsh ollisions y dynmilly moving the items mong hsh tles. Suh sheme ensures more even distriution of dt items mong hsh tles thn using only one hsh funtion. Due to the slient feture of flt ddressing with onstnt-sle ompleity, ukoo hshing needs to proe the hshed ukets only one nd otins the query results. Even in the worst se, the ukoo hshing gurntees onstnt-sle query time ompleity nd onstnt mortized time for insertions nd deletions. Cukoo hshing thus improves spe utiliztion without the inrese of query lteny. In prtie, due to the essentil property of hsh funtions, the ukoo hshing fils to fully void the hsh ollisions. Eisting work to hndle hsh ollisions minly leverges rndom-wlk pproh [3], [4], whih suffers from redundnt migrtion opertions mong servers on ount of unpreditle rndom seletion. The rndom-wlk shemes use endless loops nd high lteny for re-onstrution of hsh tles. In order to deliver high performne nd support reltime queries, we need to del with three min hllenges. Intensive Dt Migrtion. When new dt items re inserted into storge servers vi ukoo hshing, kikingout opertion my inur intensive dt migrtion mong servers [5]. The kiking-out opertion needs to migrte seleted item to its other ndidtes nd kik out nother eisting item until n empty slot is found. Frequent kiking-out opertions use intensive dt migrtion - mong multiple ukets of hsh tles. Conventionl ukoo hshing sed shemes hevily depend on the timeout sttus to identify n insertion filure. They omplete the insertion only fter eperiening rndom-wlk sed kiking-out opertions, thus resulting in endless loops nd onsuming sustntil system resoures. Hene, we need to void or llevite the ourrene of endless loops. Spe Ineffiieny. When dt ollisions our during the insertion proess, we nnot predit in dvne whether there eists dt in the slot we hoose rndomly. Beuse of the unpreditle rndom seletion of trditionl ukoo hshing, there is lwys some smll ut prtilly signifint proility tht during the dt insertion, none of the d ukets re or n esily e mde

2 empty to hold the dt, using insertion filure [6]. In this se, n epensive rehshing of ll items in the hsh tles or etr spe to store insertion filure items is required in onventionl ukoo hshing. Nevertheless, it leds to spe ineffiieny of hsh tles nd signifintly impt on the verge performne. High Insertion Lteny. The ukoo hshing shemes sed on rndom-wlk pproh migrte items rndomly mong their d ndidte positions [4]. This eertes the unertinty of hsh ddressing when ll ndidte positions re oupied. The rndom seletion in kiking-out opertions my use repetitions nd infinite loops [7], whih results in high lteny of insertion opertions. In order to ddress these hllenges, we propose Min- Counter sheme for loud storge systems to mitigte the tul hsh ollisions nd high-lteny in the insertion proess. MinCounter llows eh item to hve d ndidte ukets. And empty uket n e hosen to store the item. In order to reord kiking-out times ourring t the uket, we llote ounter for eh uket. If ll ukets re not empty, the item selets the uket with the minimum ounter to kik out the oupied item to redue or void endless loop. The rtionle of MinCounter is voiding usy routes nd seeking the empty ukets s quikly s possile. Moreover, in order to redue the frequeny of rehshing, we temporrily store the items with insertion filure into in-memory he, rther thn diretly rehsh the entire struture. The rest of this pper is orgnized s follows. Setion II shows the reserh kgrounds. Setion III presents the Min- Counter design nd prtil opertions. Setion IV illustrtes the performne evlution nd Setion V shows the relted work. Finlly, we onlude our pper in Setion VI. II. BACKGROUNDS In this setion, we present the reserh kgrounds of the ukoo hshing sheme. The ukoo hshing ws desried in [8] s dynmiztion of stti ditionry. The ditionry leverges two hsh tles, T 1 nd T 2, insted of only one, nd two hsh funtions h 1,h 2 : U {,...,r 1}, wherer is the length of eh hsh tle. Eh item S is stored in one of the ukets h 1 () in T 1 nd the ukets h 2 () in T 2. For generl lookup, we only hek whether the queried item is in one of its ndidte ukets. For dt insertion, in order to hndle hsh ollisions, ukoo hshing uses kiking-out opertions mong the ukets [9]. The ukoo hshing mkes use of d 2 hsh tles. Eh hsh tle hs n independent hsh funtion, nd eh item hs d ndidte ukets to llevite hsh ollisions. A hsh ollision ours when ll ndidte ukets of newly inserted item hve een oupied. Cukoo hshing needs to eeute kiking-out opertions to dynmilly move the eisting items of the hshed ukets nd selet suitle uket for the new item. The kiking-out opertion is similr to the ehvior of ukoo irds in nture, whih kiks other eggs or young irds out of the nest. In the similr mnner, the ukoo hshing reursively kiks items out of their ukets nd leverges multiple hsh funtions to offer multiple hoies nd llevites hsh ollisions. The ukoo hshing is dynmiztion of stti ditionry nd supports fst queries with the worst-se onstnt-sle lookup time due to flt ddressing for n item mong multiple hoies. Figure 1 shows n emple (i.e., d = 2) to illustrte the prtil opertions of stndrd ukoo hshing. We use rrows to show possile destintions for moving items s shown in Figure 1(). If item is inserted into hsh tles, we first hek whether there eists ny empty uket of ll ndidtes of item. If not, we rndomly hoose one from ndidtes nd kik out the originl item. The kiked-out item is inserted into Tle 2 in the sme wy. The proess is eeuted in n itertive mnner, until ll items find their ukets. Figure 1() demonstrtes the running proess tht the item is suessfully inserted into the Tle 1 y moving items nd from one tle to the other. While, s shown in Figure 1(), endless loops my our nd some items fil to find suitle uket to e stored. Therefore, threshold MLoop is neessry to speify the numer of itertions. If the itertion times re equl to the pre-defined threshold, we n determine the ourrene of endless loops, whih uses the entire struture re-onstrution. The theoretil nlysis of MLoop hs een shown in Setion 4.1 of [9]. Moreover, due to essentil property of rndom hoie in hsh funtions, the hsh ollision n not e fully voided, ut signifintly llevited [4]. () Initiliztion. d e f () Endless loops. d () Suessful insertion. d Fig. 1. The emple of item insertion in the ukoo hshing. III. DESIGN AND IMPLEMENTATION DETAILS In this setion, we present ost-effetive insertion sheme, lled MinCounter, to insert items in the ukoo hshing. Min-

3 Counter selets the old ukets to llevite the ourrene of endless loops in the dt insertion when hsh ollisions our. It is esy to understnd the se of d = 2 in the ukoo hshing. Eh uket ontins one item. When n item is kiked out, it hs to hoose to kik out the item in the other ndidte uket due to voiding self-kiking-out [9], []. In rel-world pplitions, the ses of d 3 re more importnt nd widely eist, whih is the fous in MinCounter. The ide ehind MinCounter is to judiiously llevite the hsh ollisions in the insertion proedure. Conventionl ukoo hshing n e rried out in only one lrge hsh tle or d 2 hsh tles. Eh item of the set S is hshed to d ndidte ukets of hsh tles. When n item is inserted into the hsh tle, we look up ll of the d ndidte ukets in order to oserve whether there is n empty one to insert. If no, we hve to reple one with the item. Thus, we hoose to use rndom-wlk ukoo hshing [3], [4] to ddress hsh ollisions. When there is no empty uket for item, it rndomly hooses the uket from its ndidtes to perform replement opertion. In generl, we void hoosing the uket tht ws repled just now due to voiding selfkiking-out. Due to the rndomness of the rndom wlk ukoo hshing, endless loops nd repetitions nnot e voided. Furthermore, we identify tht the frequeny of kiking-out in eh uket of hsh tles is not uniform. Some ukets reeives more kiking-out opertions thn others. We ll the ukets where hsh ollisions our frequently s hot ukets, nd the ukets where hsh ollisions our infrequently s old ukets. The frequeny is interpreted s the times of hsh ollisions ourring in the uket during insertion opertions. We tke dvntge of the hrteristi to propose n effetive sheme, lled MinCounter, to del with hsh ollisions. A. The Dt Struture of MinCounter MinCounter is multi-hoie hshing sheme to ple items s shown in Figure 2. It uses ukoo hshing to llow eh item to hve d ndidte ukets. An item n hoose n empty uket to lote. The used hsh funtions re stndrd (uniform nd rndom). We llote ounter for eh uket to reord the kiking-out times ourring t the uket. If no empty ukets re ville, the item needs to selet one with the minimum ounter to kik out the oupied item to redue or void endless loop. We temporrily store insertion-filure items into he rther thn rehsh the struture immeditely to redue the filure proility of entire item insertion. Figure 2 illustrtes the dt struture of MinCounter. The lue ukets re the hit positions y hsh omputtion. If ll positions h i () re oupied y other items, the item hve to reple one through the MinCounter sheme. Furthermore, the item hs to e inserted into the etr he when insertion filure ours. B. The MinCounter Working Sheme In order to llevite the ourrene of endless loops in ukoo hshing, we improve the onventionl ukoo hshing Che If filing h1() Fig. 2. h3() h2() The dt struture of MinCounter. Tle3 y lloting ounter for eh uket of hsh tles. We utilize the ounters to reord kiking-out times of ukets in history. When hsh ollision ours in uket, the orresponding ounter inreses y 1. If n item is inserted into the hsh tles without the vilility of empty ndidte ukets, we hoose the uket with the minimum ounter to eeute the replement. As shown in Figure 3, we tke d = 3togivenemple. When the item is inserted into hsh tles, we first hek the ukets of h 1 (), h 2 (), h 3 () in eh hsh tle respetively to find n empty uket. Eh ndidte uket of is oupied y,, respetively (Figure 3()). Moreover, we ompre the ounters of ndidte ukets nd hoose the minimum one (i.e., 18 in this emple), nd further reple item with. In the mentime, the ounter of the uket of h 3 () inreses y 1 up to 19 (Figure 3()). The kiked-out item eomes the one needed to e inserted, nd the insertion proedure goes on, until n empty slot is found in hsh tles. h1() Fig. 3. h3() h2() () Initil sttus. () Running sttus. Tle3 Tle3 The stndrd ukoo hshing tle struture.

4 C. Hndling Endless Loops MinCounter llows items to e inserted into hsh tles to improve the storge spe effiieny, ut fils to fully ddress hsh ollisions. Like ChunkStsh [6], we leverge n etr spe to temporrily store the dt tht use hsh ollisions rther thn rehsh the struture. For query, we need to hek oth the hsh tles nd the stsh to gurntee the query ury. IV. PERFORMANCE EVALUATION In this setion, we evlute the performne of the designed MinCounter sheme y implementing prototype under lrge-sle loud omputing environment. The evlution metris minly inlude the utiliztion rtio of hsh tles when insertion filures our, nd totl kiking-out times fter ompleting entire item insertion. The utiliztion rtio of hsh tles is interpreted s the proportion of the oupied ukets to ll ukets of hsh tles when insertion filure ours. A. Eperimentl Setup We implement the MinCounter sheme in lrge-sle loud omputing environment. The prototype is developed under the Linu kernel environment nd we implement ll funtionl omponents of MinCounter in the user spe. Eh server is equipped with Intel 2.4GHz qud-ore CPU, 16GB DRAM, 5GB disk. In order to demonstrte the effiieny nd effetiveness of the proposed MinCounter sheme, we use 2 dtsets nd 2 initil rtes, i.e., 1.1 nd 2.4, in hsh tles. The initil rte mens the multiple we set sed on sizes of dtset to rete hsh tles. When the rte is 1.1, hsh ollisions often our, nd hrdly when the rte is ) The Dtset of Rndomly Generted Numers: In order to omprehensively emine the performne of the proposed MinCounter sheme, we first present the theoretil nlysis results in terms of rndomness y using n open-soure rndom numer genertor to generte integer dtsets s shown in Tle I. We further present the performne improvements y using the tre from rel-world pplitions. TABLE I THE DATASET OF RANDOMLY GENERATED NUMBERS. Groups Rnge Size group group group group group group ) The Rel-world Tre: Bg of Words: This tre ontins four tet olletions in the form of gs-of-words. For eh tet olletion, D is the numer of douments, W is the numer of words in the voulry, nd N is the totl numer of words in the olletion. The detils re shown in Tle II. We tke dvntge of the union of doid nd wordid s keys of items to e inserted into hsh tles. TABLE II THE BAG OF WORDS TRACES. Groups Tet olletions D W N group1 KOS log entries group2 NIFS full ppers group3 Enron Emils group4 NYTimes news rtiles B. The Kiking-out Threshold Settings Eisting ukoo hshing shemes fil to fully void endless loops due to the essentil property of hsh ollisions. In order to llevite the endless loops nd redue temporl nd sptil overheds in the item insertion opertions, onventionl method is to pre-define n pproprite threshold to represent the tolerle mimum times of kiking-out per insertion opertion. However, it is nontrivil to otin the suitle threshold vlue tht depends on the pplition requirements nd system sttus. In order to rry out meningful eperiments, we hoose to use severl threshold, 5, 8, nd 1, to proess the following eperiments. C. The Counter Size Settings First, we need to onsider the its per ounter of per uket in hsh tles for spe svings. We rndomly hoose two groups of dt from 2 dtsets respetively for sttisti nlysis. Most vlues re distriuted in the intervl of to 32 (nmely 2 5 ). The vlues of ounters lrger thn 32 re, nd it is suffiient to llote 5 its per ounter. The memory overflow my hrdly our, whih mens MinCounter leds to the equilirium distriution. To demonstrte the effiieny of our MinCounter sheme, Figure 4 shows the its per ounter nd the verge numers of kiking-out times per uket in hsh tles when using the MinCounter sheme. We oserve tht t most 5 its per uket is suffiient for lrge proportion of dtset. The length of ounter(it) RndNum1 RndNum2 BgofWords1 BgofWords2 Fig. 4. length Dtsets men numer The distriution of vlues of ounters The men numer of kiking-out times D. Eperimentl Results We show dvntges of MinCounter over RndomWlk [4] nd ChunkStsh [7] y ompring their eperimentl results in terms of utiliztion rtio of hsh tles nd totl kiking-out times during insertion opertions. The thresholds of kikingout times re 5, 8, nd 1. MT is the threshold of kiking-out times in the MinCounter sheme, RT is the threshold in the RndomWlk sheme nd CT is the threshold in the

5 ChunkStsh sheme. Menwhile, numers ehind MT, RT nd CT in following figures re thresholds set in eperiments, suh s MT8 is the MinCounter sheme with the threshold of 8. 1) The Results of using Rndomly Generted Numers: Figure 5 shows the utiliztion rtio of ukoo hsh tles when insertion filure first ours y using the tre of rndomly generted numers. We oserve tht the verge utiliztion rtio of MinCounter is 75% in the tre of rndomly generted numers, whih is higher thn the perentge of 7% in RndomWlk. Compred with the RndomWlk sheme, MinCounter otins on verge 5% utiliztion rtio promotion. RndomWlk sheme needs to hoose kiking-out positions rndomly when hsh ollisions our. There is no guide for voiding endless loops, nd itertions my esily reh the threshold of kiking-out times. Less items n e inserted into hsh tles, whih results in lower utiliztion rtio of hsh tles. Furthermore, n insertion filure shows the ourrene of n endless loop. A rehsh proess is needed. MinCounter improves the utiliztion rtio of hsh tles, whih mens the proposed sheme llevites hsh ollisions nd dereses the rehsh proility. MinCounter optimizes the loud omputing systems performne y improving the utiliztion of hsh tle nd deresing the rehsh proility. We emine the totl kiking-out times of MinCounter nd ChunkStsh y using the metri of totl kiking-out numers in the tre of rndomly generted numers s shown in Figure 6. When insertion filure ours, we store the item into temporry smll dditionl onstnt-size he like ChunkStsh rther thn rehsh tles immeditely. This my use slight etr spe overhed, ut otin the enefits of reduing the filure proility. Compred with ChunkStsh, MinCouter signifintly uts down over % totl kiking-out numers in rte = 1.1 (in Figure 7) nd on verge 37% in rte = 2.4 (in Figure 6()). MinCounter enhnes the eperienes of loud users through deresing totl kiking-out times. The utiliztion rtio of hsh tles MT5 RT5 MT8 RT8 MT RT MT1 RT1 Rndomly Generted Numers Fig. 5. The utiliztion rtio of ukoo hsh tles using the tre of rndomly generted numers. 2) The Results of using Bg of Words Tre: Figure 8 illustrtes the utiliztion rtio of ukoo hsh tles when using the g of words tre. We oserve tht MinCounter otins on verge 5% utiliztion improvement, ompred with RndomWlk sheme, while the verge utiliztion rtio of MinCounter is 88% in the Bg of Words tre, nd 83% in Rndom-Wlk sheme. Figure 9 shows the totl kikingout numers in the g of words tre. Compred with Totl kiking-out numers(million) Totl kiking-out numers(million) MT5 CT5 MT8 CT8 MT CT MT1 CT Rndomly Generted Numers () Rte = 1.1. MinCounter ChunkStsh MinCounter vs ChunkStsh Rndomly Generted Numers () Rte = Deresing rtio(%) Fig. 6. The totl kiking-out numers of whole insertion opertions using the tre of rndomly generted numers. Deresing rtio(%) MT5vsCT5 MT8vsCT8 MTvsCT MT1vsCT Rndomly Generted Numers Fig. 7. The deresing rtio of totl kiking-out times of MinCounter using the tre of rndomly generted numers in rte = 1.1. ChunkStsh, MinCouter signifintly redues lmost 5% totl kiking-out numers in rte = 1.1 (in Figure ), nd on verge % in rte = 2.4 (in Figure 9()). E. Summry Eperimentl results demonstrte MinCounter hs the dvntges in terms of the utiliztion rtio of hsh tles nd the totl kiking-out times. MinCounter n effiiently improve the utiliztion of ukoo hsh tles nd derese the rehsh proility to optimize the loud omputing systems performne. Menwhile, it enhnes eperiene of loud users through deresing the totl kiking-out times. V. RELATED WORK Cukoo hshing [9] is n effiient vrition of the multihoie hshing sheme. In the ukoo hshing sheme, n

6 The utiliztion rtio of hsh tles MT5 RT5 MT8 RT8 MT RT MT1 RT Bg of Words Fig. 8. The utiliztion rtio of ukoo hsh tles using the tre of Bg of Words. Totl kiking-out numers (thousnd) MT5 CT5 MT8 CT8 MT CT MT1 CT1 Bg of Words () Rte = 1.1. MinCounter ChunkStsh MinCounter vs ChunkStsh Totl kiking-out numers(thousnd) Bg of Words () Rte = Deresing rtio(%) Fig. 9. The totl kiking-out numers of whole insertion opertions using the tre of Bg of Words. item n e pled in one of multi-ndidte ukets of hsh tles. When there is no empty uket for n item t ny of its ndidtes, the item n kik out the item eisting in one of the ukets, insted of using insertion filure nd overflow (e.g., using the linked lists). The kiked-out item opertes in the sme wy, nd so forth itertively, until ll items oupy one of ukets during insertion opertions. Some reserhes disuss the se of multiple seletle hoies of d > 2s hypergrphs [11], [12]. Eisting work out ukoo hshing [13], [14] presents the theoretil nlysis results. Simple properties of rnhing proesses re nlyzed in iprtite grph [13]. A study y M. Mitzenmher judiiously nswers the open questions to ukoo hshing [14]. Further vritions of ukoo hshing re onsidered in Re- Deresing rtio(%) MT5vsCT5 MT8vsCT8 MTvsCT MT1vsCT Bg of Words Fig.. The deresing rtio of totl kiking-out times of MinCounter using the tre of Bg of Words in rte = 1.1. f. [4], [6], [15]. For hndling hsh ollisions without redthfirst serh nlysis, the study y A. Frieze et l. presents more effiient method lled rndom-wlk. This method rndomly selets one of ndidte ukets for the inserted item, if there is no vny mong its possile lotions [4]. In order to drmtilly redue the proility tht filure ours during the insertion of n item, they propose more roust hshing, tht is ukoo hshing with smll onstnt-sized stsh, nd demonstrte tht the size of stsh is equivlent to only three or four items nd it hs tremendous improvements through nlytilly nd through simultions [6]. Nekle [15] is n effiient vrition of ukoo hshing sheme to mitigte hsh ollisions in insertion opertions. Cukoo hshing hs een widely used in rel-world pplitions [7], [16], [17]. Cukoo hshing is menle to hrdwre implementtion, suh s in router. To void lrge numer of items to e moved during insertion opertions using epensive overhed in hrdwre implementtion, t most one item to e moved is eptle [16]. ChunkStsh [7] improves dvntges of vrint of ukoo hshing to resolve hsh ollisions, whih indees hunk metdt using n in-memory hsh tle. NEST [17] leverges ukoo-driven hshing to hieve lod lne. VI. CONCLUSION In order to llevite the ourrene of endless loops, this pper proposed novel ukoo hshing sheme, nmed MinCounter, for lrge-sle loud omputing systems. The MinCounter hs the ontriutions to three min hllenges in hsh-sed dt strutures, i.e., intensive dt migrtion, low spe utiliztion nd high insertion lteny. MinCounter tkes dvntge of old ukets to llevite hsh ollisions nd derese insertion lteny. MinCounter optimizes the performne for loud servers, nd enhnes the qulity of eperiene for loud users. Compred with stte-of-the-rt work, we leverge etensive eperiments nd rel-world tres to demonstrte the enefits of MinCounter. ACKNOWLEDGMENT This work ws supported in prt y Ntionl Bsi Reserh 973 Progrm of Chin under Grnt 11CB21 nd Ntionl Nturl Siene Foundtion of Chin(NSFC) under Grnt nd

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