The Optimality of Distributed Constructions of Minimum Weigth and Degree Restricted Spanning Trees in a Complete Network of Processors

Abstract

F i n d i n g s p a n n i n g t r e e s b e c a m e a c e n t r a l r e s e a r c h i s s u e in d i s t r i b u t e d n e t w o r k s a n d c o m m u n i c a t i o n p r o t o c o l s , a s m o s t a l g o r i t h m s f o r t h e s e e n v i r o n m e n t s , in a g e n e r a l n e t w o r k s t r u c t u r e , a s s u m e a n u n d e r l y i n g s t r u c t u r e of a s p a n n i n g t r e e , on w h o s e e d g e s a l l c o m m u n i c a t i o n a c t i v i t i e s t a k e p l a c e . U s i n g s u c h a t r e e i t is e a s y t o d i s t i n g u i s h o n e p r o c e s s o r as a l e a d e r , p a s s a t o k e n in t h e n e t w o r k {a t e c h n i q u e w i d e l y u s e d in t h e s e e n v i r o n m e n t s to a s s u r e m u t u a l e x c l u s i o n , t o c h e c k t e r m i n a t i o n , e t c . ) , b r o a d c a s t m e s s a g e s , a n d o t h e r r e l a t e d a p p l i c a t i o n s . In t h i s w o r k we p r e s e n t two l o w e r b o u n d s o n t h e a m o u n t of c o m m u n i c a t i o n a c t i v i t i e s n e e d e d in o r d e r t o c o n s t r u c t s p a n n i n g t r e e s w i th s p e c i a l p r o p e r t i e s in a c o m p l e t e n e t w o r k . In [1] a d i s t r i b u t e d a l g o r i t h m for c o n s t r u c t i n g a m i n i m u m s p a n n i n g t r e e i s con s t r u c t e d , a n d t h e q u e s t i o n is r a i s e d t h e r e w h e t h e r f i nd ing a n y s p a n n i n g t r e e is e a s i e r t h a n f ind ing a m i n i m u m w e i g h t one . One of t h e l o w e r b o u n d s p r e s e n t e d h e r e a n s w e r s t h i s q u e s t i o n . In c e r t a i n a p p l i c a t i o n s i t is d e s i r e d t h a t t h e n o d e s of t h e s p a n n i n g t r e e will h a v e b o u n d e d d e g r e e s , in o r d e r t o p r e v e n t b o t t l e n e c k e f f e c t s a n d o v e r c o m e p h y s i c a l r e s t r i c t i o n s in t h e c o m m u n i c a t i o n n e t w o r k . Our s e c o n d b o u n d is r e l a t e d t o t h i s p r o b l e m . This work wax done while th i s a u t h o r was a t IBM Is rae l ~cient i f ic Cen te r . Permission to copy without fcc all or part of this matcria| is granted provided that thc copics arc not madc or distributed for direct commercial advantagc, thc ACM copyright notice and thc tit|c of the publication and its date appear, and noticc is givcn that copying is by pcrmission of thc Association for Computing Machinery. To copy othcrwisc, or to republish, rcquircs a fcc and/or specific permission. ©1985 ACM 0-89791-167-9/1985/0800-0277 $00.75

DOI: 10.1145/323596.323622

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@inproceedings{Korach1985TheOO, title={The Optimality of Distributed Constructions of Minimum Weigth and Degree Restricted Spanning Trees in a Complete Network of Processors}, author={Ephraim Korach and Shlomo Moran and Shmuel Zaks}, booktitle={PODC}, year={1985} }