Breuer Algorithm

# Breuer Algorithm - A CLASS OF MI N CUT PLACEMENT ALGORI...

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Unformatted text preview: A CLASS OF MI N- CUT PLACEMENT ALGORI THMS % by Mel vi n A. Br euer Depar t ment s of El ect r i cal Engi neer i ng g~ Comput er Sci ence Uni ver s i t y of Sout her n Cal i f or ni a Los Angel es , Cal i f or ni a 90007 Summa r y In t hi s paper we pr es ent a cl as s of r ai n- cut pl ace- ment al gor i t hms for s ol vi ng s ome as s i gnment pr ob- l ems r el at ed to the phys i cal i mpl ement at i on of el ec- t r i cal ci r cui t s . We di s cus s t he need f or abandoni ng cl as s i cal obj ect i ve f unct i ons bas ed upon di s t ance, and i nt r oduce new obj ect i ve f unct i ons bas ed upon "s i gnal s - cut. " The number of s i gnal s cut by a line c is a l ower bound on the number of r out i ng t r acks whi ch mus t cr os s c in r out i ng t he ci r cui t . Thr ee s peci f i c obj ec- t i ve f unct i ons ar e i nt r oduced and the r el at i ons hi p be- t ween one of t hes e and a cl as s i cal di s t ance meas ur e bas ed upon hal f - per i met er is pr es ent ed. Two r ai n- cut pl acement al gor i t hms ar e pr es ent ed. They ar e r ef er r ed to as C) uadr at ur e and Sl i ce/ Bi s ec- tion. The concept s of a bl ock and cut line ar e i nt r o- duced. Thes e two ent i t i es ar e the maj or cons t r uct s in devel opi ng any new mi n- cut pl acement al gor i t hm. Mos t of t he concept s pr es ent ed have been i mpl e- ment ed, and s ome exper i ment al r es ul t s ar e gi ven. I. I nt r oduct i on Thi s paper deal s wi t h a cl as s i cal pr obl em encoun- t er ed in the phys i cal i mpl ement at i on of ci r cui t car ds or chi ps , r ef er r ed to as the pl acement pr obl em. The pr obl em is def i ned, s emi f or mal l y, as f ol l ows . Gi v- en a s et of el ement s 8 = {el, e~ . . . . . e~} and a s et of s i gnal s ,2= [ s u sm . . . . . s , }. We as s oci at e wi t h each el ement e E ~ a s et of s i gnal s ,2e, wher e J~ = J. Si mi - l ar l y wi t h each s i gnal s E • we as s oci at e a s et of el e- ment s e,, where \$ ={else ,/,}. d~, is said to be a signal net. We are also given a set of slots or loca- tions ~=[LI, L m ..... L ], where pgn. The place- ment problem is to assign each e l~ ~ to a unique lo- cation Lj such that some objective is optimized. Nor- mally each element is considered to be a point, and if e t is assigned to location L~ then its position is de- fined by the coordinate values (x],y~). Usually a sub- set of the elements in d~ are fixed, i.e., pre-assigned to locations, and only the remaining elements can be assigned to the remaining unassigned locations. Non fixed elements are called moveable elements, and those slots not pre-assigned elements are called open slots. Example placement problems deal with polycell LSI chip design [2,4,5], PC card design, and assign- ing functions to previously placed IC's....
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## This note was uploaded on 11/21/2009 for the course ESE 556 taught by Professor Doboli,a during the Fall '08 term at SUNY Stony Brook.

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Breuer Algorithm - A CLASS OF MI N CUT PLACEMENT ALGORI...

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