New bounds for the controller problem

Yuval Emek, Amos Korman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The (M, W)-controller, originally studied by Afek, Awerbuch, Plotkin, and Saks, is a basic distributed tool that provides an abstraction for managing the consumption of a global resource in a distributed dynamic network. The input to the controller arrives online in the form of requests presented at arbitrary nodes. A request presented at node u corresponds to the "desire" of some entity to consume one unit of the global resource at u and the controller should handle this request within finite time by either granting it with a permit or denying it. Initially, M permits (corresponding to M units of the global resource) are stored at a designated root node. Throughout the execution permits can be transported from place to place along the network's links so that they can be granted to requests presented at various nodes; when a permit is granted to some request, it is eliminated from the network. The fundamental rule of an (M, W)-controller is that a request should not be denied unless it is certain that at least M-W permits are eventually granted. The most efficient (M, W)-controller known to date has message complexity , where N is the number of nodes that ever existed in the network (the dynamic network may undergo node insertions and deletions). In this paper we establish two new lower bounds on the message complexity of the controller problem. We first prove a simple lower bound stating that any (M, W)-controller must send messages. Second, for the important case when W is proportional to M (this is the common case in most applications), we use a surprising reduction from the (centralized) monotonic labeling problem to show that any (M, W)-controller must send messages. In fact, under a long lasting conjecture regarding the complexity of the monotonic labeling problem, this lower bound is improved to a tight . The proof of this lower bound requires that N=O (M) which turns out to be somewhat inevitable due to a new construction of an (M, M / 2) -controller with message complexity O (N log2 M) .

Original languageEnglish
Title of host publicationDistributed Computing - 23rd International Symposium, DISC 2009, Proceedings
Number of pages13
StatePublished - 2009
Externally publishedYes
Event23rd International Symposium on Distributed Computing, DISC 2009 - Elche, Spain
Duration: 23 Sep 200925 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5805 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Symposium on Distributed Computing, DISC 2009

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


Dive into the research topics of 'New bounds for the controller problem'. Together they form a unique fingerprint.

Cite this