Метод уменьшения сложности графа задержек коммуникационной среды вычислительного кластера (Method for reducing graph of communication delays in for visual analysis)

(1)

Ìåòîä óìåíüøåíèÿ ñëîæíîñòè ãðàà çàäåðæåê

êîììóíèêàöèîííîé ñðåäû âû÷èñëèòåëüíîãî êëàñòåðà

Í.Î. Æóêîâ, À.Í. Ñàëüíèêîâ

ÌÓ èìåíè Ì.Â. Ëîìîíîñîâà

Âäàííûéìîìåíòóùåñòâóåòïðîáëåìàîòîáðàæåíèÿèíîðìàöèèîçàäåðæêàõâêîììó-

íèêàöèîííîéñðåäå.Îòîáðàæåíèåòàêîéèíîðìàöèèââèäåîðèåíòèðîâàííîãîâçâåøåííîãî

ãðàà äà¼ò âîçìîæíîñòè äëÿ âèçóàëüíîãîàíàëèçà õàðàêòåðèñòèê êîììóíèêàöèîííîé ñðå-

äû. Îäíàêî ïðè òàêîì ïîäõîäå ìû ïîëó÷àåì ãðà îãðîìíîãî ðàñìåðà, ñ î÷åíü áîëüøèì

÷èñëîì ð¼áåð.

Âàæíûì ñ ïðàêòè÷åñêîé òî÷êè çðåíèÿ ÿâëÿåòñÿ òî, ÷òî ÷åì áûñòðåå áóäåò ïîñòðîåí

ãðà òîïîëîãèè ñóïåðêîìïüþòåðà, ÷åì áîëåå íàãëÿäíà áóäåò âèçóàëèçàöèÿ, òåì áûñòðåå

áóäåò íàéäåíà îøèáêà èëè íåïîëàäêà â ðàáîòå âû÷èñëèòåëüíîãî êëàñòåðà. Òàê æå áóäåò

ïðîùå èñïîëüçîâàòü êëàñòåð ñ ìàêñèìàëüíîé ïðîèçâîäèòåëüíîñòüþ, òàê êàê áóäåò ïðîùå

ïîäîãíàòüïðîãðàììó ïîä àðõèòåêòóðóêîíêðåòíîãî âû÷èñëèòåëüíîãîêëàñòåðà.

Â ïðåäûäóùåé ðàáîòå [1℄ áûë ïðåäëîæåí ìåòîä, êîãäà ãðà çàäåðæåê â êîììóíèêà-

öèîííîé ñðåäå îòîáðàæàåòñÿ â òð¼õìåðíîì ïðîñòðàíñòâå ñëåäóþùèì îáðàçîì: æäîé âåð-

øèíå ñòàâèòñÿâñîîòâåòñòâèåòî÷êà ñòð¼õìåðíûìèêîîðäèíàòàìè,àðåáðîïðåäñòàâëÿåòñÿ

â âèäå îòðåçêà, ñîåäèíÿþùåãî äâå ñîîòâåòñòâóþùèå âåðøèíû (òî÷êè). Äëèíû âñåõ îòðåç-

êîâ ïðîïîðöèîíàëüíû âåëè÷åíå çàäåðæêèïðè ïåðåäà÷å.Îòîáðàæåíèåñòðîèòñÿ ïðè ïîìî-

ùè ìåòîäà ìíîãîìåðíîãîøêàëèðîâàíèÿ. Ïðåäëîæåííûéìåòîä èíòåãðèðîâàí ñ ïðîãðàììó

network_viewer2 [2℄.

Ïðåäïîëàãàåìûé â äàííîé ðàáîòå ìåòîä îñóùåñòâëÿåò ïðåäâàðèòåëüíîå ñæàòèå ãðà-

à, Ñæàòèåâûïîëíÿåòñÿâ íåñêîëüêîýòàïîâ.Âíà÷àëåãðà ðàçáèâàåòñÿ,èñïîëüçóÿ ñïåöè-

àëüíûå àëãîðèòìû ðàçáèåíèÿãðàîâ, çàòåì ïîäãðà âñå âåðøèíû êîòîðîãî ïðèíàäëåæàò

îäíîéãðóïïå ñæèìàþòñÿâ âåðøèíó.Àëãîðèòìïàðàìåòðèçîâàí ïàðàìåòðîì¾ñòåïåíüñæà-

òèÿ¿, êîòîðûé çàäà¼ò äîïóñòèìóþ ðàçíèöó ìåæäó ðàññòîÿíèìè âíóòðè ãðóïïû âåðøèí è

ìåæäó ãðóïïàìè. Â èíòåðåéñå ïðîãðàììû network_viewer2 äëÿ áîëåå äåòàëüíîãî ïðî-

ñìîòðà ãðàà ðåàëèçóåòñÿ âîçìîæíîñòü ðàñêðûòèÿ âåðøèíû, ñîîòâåòñòâóþùåé ãðóïïå â

êîòîðóþ áûëñæàòïîäãðà.Êìåòîäóïðåäúÿâëÿþòñÿñëåäóþùèåòðåáîâàíèÿ:

1. ñîõðàíåíèå îòíîñèòåëüíîéäëèíûäóããðàà;

2. ðàçáèâàåòñÿ ãðà òàêèì îáðàçîì, ÷òî ñóììà âåñîâ ðåáåð âíóòðè ïîäãðàà ìåíüøå,

÷åì ìåæäóïîäãðàîì èäðóãèìèðåáðàìè ãðàà;

3. âåñðåáðàìåæäóäâóìÿâåðøèíàìèâñæàòîìãðàååñòüñðåäíååàðèìåòè÷åñêîåâñåõ

âåñîâ ðåáåð,ñîåäèíÿþùèõâñåâåðøèíû âäàííûõïîäãðààõ.

Òàê æå äëÿ âûÿâëåíèÿ èåðàðõè÷åñêîé ñòðóêòóðû ãðàà ðåàëèçóåòñÿ ìåòîä ñæàòèÿ, îñíî-

âàííûé íàèåðàðõè÷åñêèõàëãîðèòìàõêëàñòåðèçàöèè.

Àëãîðèòì ðàáîòàåò íà ïîñòðîåíèè èåðàðõè÷åñêèõ ìíîæåñòâ. Íà êàæäîì øàãå ïðîèç-

âîäèòñÿ ðàçáèåíèå ãðàà íà ìíîæåñòâî ïîäãðàîâ. Çäåñüñòðîèòñÿ ìàññèâ, ãäå ýëåìåíò

ýòî íîìåð êëàñòåðàâ ñëåäóþùåé èåðàðõèè. Ïðîöåññïðîäîëæàåòñÿäî òåõ ïîð,ïîêà ÷èñëî

âåðøèííå äîñòèãíåòóêàçàííîãî ïîëüçîâàòåëåìâ ïàðàìåòðàõ àëãîðèòìà.Âäàëüíåéøåì,â

ðàìêàõ ïðîöåäóðû ¾ðàñêðûòèÿ âåðøèíû¿ â ãðà äîáàâëÿþòñÿ âåðøèíû äëÿ êëàñòåðà èç

ïðåäûäóùåé èåðàðõèè.

åàëèçàöèÿàëãîðèòìîââûïîëíåíàíà ÿçûêàõÑ,C++,ãðàè÷åñêèéïîëüçîâàòåëüñêèé

èíòåðåéñ íàïèñàí ñ èñïîëüçîâàíèåì êðîññïëàòîðìåííîé áèáëèîòåêè Qt. Âèçóàëèçàöèÿ

ãðàîâïðîèñõîäèòñïîìîùüþáèáëèîòåêèOpenGL,óíêöèîíàëêîòîðîéïðåäîñòàâëåíQt-

ìîäóëåìQtOpenGL.

Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org

583

(2)

àáîòàïðîãðàììûîïðîáîâàíàíàäàííûõçàäåðæåêïîëó÷åíûõññóïåðêîìïüþòåðà¾Ëî-

ìîíîñîâ¿ äëÿ 1000 óçëîâ, ÷òî ñîîòâåòñòâóåò ÷åòâ¼ðòîé ÷àñòè âñåõ óçëîâ îáùåäîñòóïíîé

î÷åðåäè¾regular4¿.

Ïðîãðàììà âðåìåííûåõàðàêòåðèñòèêèðàáîòû ïðåäñòàâëåíû â òàáëèöàõ 1è 2.

Òàáëèöà1: âðåìÿðàáîòû ïðîãðàììûâ çàâèñèìîñòèîò ÷èñëàð¼áåð

×èñëî ðàçáèåíèé ÷èñëîð¼áåð âðåìÿ (ìñ.)

0(ïîëíûéãðà) 123064 1968254

100 4465 >400

50 1225 >100

10 45 >10

Òàáëèöà2:âðåìÿðàáîòû àëãîðèòìàêëàñòåðèçàöèè âçàâèñèìîñòè îò ñîîòíîøåíèÿ

ðàçíîñòè ðàññòîÿíèé âíóòðèêëàñòåðàè ñíàðóæè

ðàçíîñòü% ÷èñëîð¼áåð âðåìÿ (ìñ.)

40 2211 29640

20 2080 27520

7 105 3230

3 3 10

Ëèòåðàòóðà

1. BannikovP.S, SalnikovA.N. Retrievingtopologyofinteronnetions inomputational

luster basedon resultsof MPIbenhmarks// MosowUniversityComputational

Mathematis andCybernetis. 2014. Vol.38, no.2.P.7382. DOI:

10.3103/S0278641914020022

2. Ñàéò ïðîåêòàïî òåñòèðîâàíèþâû÷èñëèòåëüíûõ êëàñòåðîâ¾ClustBenh¿:

URL: https://github.om/lustbenh/network-tests2 (Äàòàîáðàùåíèÿ15.06.2015)

Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org

584

(3)

Method for reducing graph of communication delays in for visual analysis

Alexey Salnikov and Nikolay Zhukov

Keywords: weighted graphs, clustering algorithm, communications delays, compute cluster There discussed methods for visualizing huge graphs where edges marked by distances between vertices. The goal is to reduce graph complexity of huge graph in context of visual analysis of delays. There we have used some methods of clusterization which save egde distances. This method usability has been tested on data about delays arrived in communications of Lomonosov supercomputer.