NDLI: Stack and Queue Layouts of Directed Acyclic Graphs: Part I

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Heath, Lenwood S. Trenk, Ann N. Pemmaraju, Sriram V.
Copyright Year	1999
Abstract	Stack layouts and queue layouts of undirected graphs have been used to model problems in fault-tolerant computing and in parallel process scheduling. However, problems in parallel process scheduling are more accurately modeled by stack and queue layouts of directed acyclic graphs (dags). A stack layout of a dag is similar to a stack layout of an undirected graph, with the additional requirement that the nodes of the dag be in some topological order. A queue layout is defined in an analogous manner. The stacknumber ( queuenumber) of a dag is the smallest number of stacks (queues) required for its stack layout (queue layout). In this paper, bounds are established on the stacknumber and queuenumber of two classes of dags: tree dags and unicyclic dags. In particular, any tree dag can be laid out in 1 stack and in at most 2 queues; and any unicyclic dag can be laid out in at most 2 stacks and in at most 2 queues. Forbidden subgraph characterizations of 1-queue tree dags and 1-queue cycle dags are also presented. Part II of this paper presents algorithmic results---in particular, linear time algorithms for recognizing 1-stack dags and 1-queue dags and proof of NP-completeness for the problem of recognizing a 4-queue dag and the problem of recognizing a 9-stack dag.
Starting Page	1510
Ending Page	1539
Page Count	30
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539795280287
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	28
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-28
Access Restriction	Subscribed
Subject Keyword	queue layout Analysis of algorithms and problem complexity dags Applications of graph theory graph embedding Graph theory stack layout directed acyclic graphs forbidden subgraph book embedding Complexity classes
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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