Bounds for the On-line Multicast Problem in Directed Graphs
نویسندگان
چکیده
On-line multicasting has received a lot of attention lately, because of its great practical importance. However, most research assumes undirected graphs, which fail to model the directivity of real networks. In this paper, we ll this gap by ooering upper and lower bounds for the on-line directed multicast problem in a worst case analysis. We examine two types of on-line problems: the join-only problem where destinations join arbitrarily but stay till the end of the session, and the join-leave problem, where destinations can join and leave arbitrarily. We deene the asymmetry of a graph to be the maximum ratio of opposite directed edges between a pair of nodes for all node-pairs. For the join-only on-line problem, we prove that a greedy on-line algorithm is log(A + 1)-competitive compared to any on-line algorithm. For the join-leave problem on both undirected and directed graphs, we prove a new lower bound, which is exponential in the previous undirected bound (the number of joins requests). We, then, show that, for highly asymmetric graphs, the ineeciency is proportional to the asymmetry, i.e., arbitrarily larger than the number of join requests.
منابع مشابه
Directed domination in oriented hypergraphs
ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...
متن کاملTwin minus domination in directed graphs
Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...
متن کاملSigned total Roman k-domination in directed graphs
Let $D$ be a finite and simple digraph with vertex set $V(D)$.A signed total Roman $k$-dominating function (STR$k$DF) on$D$ is a function $f:V(D)rightarrow{-1, 1, 2}$ satisfying the conditionsthat (i) $sum_{xin N^{-}(v)}f(x)ge k$ for each$vin V(D)$, where $N^{-}(v)$ consists of all vertices of $D$ fromwhich arcs go into $v$, and (ii) every vertex $u$ for which$f(u)=-1$ has a...
متن کاملOn-line Multicasting in Directed Graphs Work in progress
In this paper we study the problem of on-line multicasting on directed graphs, and we demonstrate the competitiveness of a greedy algorithm in a worst case analysis. We prove that the greedy algorithm performs almost as well as any on-line algorithm: the greedy upper bound is very close to the lower bound of any on-line algorithm. First, we improve on the upper bound of the oo-line greedy algor...
متن کاملA New Method based on Intelligent Water Drops for Multicast Routing in Wireless Mesh Networks
In recent years a new type of wireless networks named wireless mesh networks has drawn the attention of researchers. In order to increase the capacity of mesh network, nodes are equipped with multiple radios tuned on multiple channels emerging multi radio multi channel wireless mesh networks. Therefore, the main challenge of these networks is how to properly assign the channels to the radios. O...
متن کامل