Citations: Stack and queue layouts of directed acyclic graphs: Part II

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L. S. Heath and S. V. Pemmaraju. Stack and queue layouts of directed acyclic graphs: Part II. SIAM Journal on Computing, 28(5):1588--1626, 1999.

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Queue Machines: Hardware Compilation in Hardware - Schmit, Levine, Ylvisaker (Correct)

....in operation in Figure 3. Machines with a single operand stack can be used to represent acyclic data flow graphs that either: have a undirected covering graph that is a tree, or have an undirected covering graph that contains at most one cycle with that cycle having a directed Hamiltonian path [3]. This is an advantage for a compiler, as most expressions are parsed as trees and convert to stack operand form easily. However, this limits the class of data flow graphs that one can successfully express. Ideally, we want a machine that can capture any directed acyclic graph (DAG) Stack ....

....a subtree can have multiple fanouts, but it does not make it possible to capture general data flow graphs without the use of a separate memory or scratch space. Programs for queue machines can represent all data flow graphs that have an embedding that is a directed arched leveled planar graph [3]. We will consider a subset of this class of graphs, DAGs with an embedding that is a leveled planar graph. A leveled graph is one in which there exists a mapping A of vertices to integers such that if there is an arc from vertex u to vertex v, then A(u) A(v) 1 for all arcs in the graph. ....

L. S. Heath, S. V. Pemmaraju, A. N. Trenk, "Stack and Queue Layouts of Directed Acyclic Graphs: Part I," SIAM J. Comput. Vol 23, No. 4, pp. 1510-1539.

Level Planarity Testing in Linear Time - Jünger, Leipert, Mutzel (1999) (1 citation) (Correct)

....direction, and no edges intersect except at their end vertices. If G has a single source, the test can be performed in O(jV j) time by an algorithm of Di Battista and Nardelli [1988] that uses the PQ tree data structure introduced by Booth and Lueker [1976] PQ trees have also been proposed by Heath and Pemmaraju [1995, 1996] to test level planarity of level directed acyclic graphs with several sources and sinks. It has been shown in Junger, Leipert, and Mutzel [1997] that this algorithm is not correct in the sense that it does not state correctly level planarity of every level planar graph. In this paper, we present ....

....is not correct in the sense that it does not state correctly level planarity of every level planar graph. In this paper, we present a correct linear time level planarity testing algorithm that is based on two main new techniques that replace the incorrect crucial parts of the algorithm of Heath and Pemmaraju [1995, 1996]. 1 Introduction A fundamental issue in Automatic Graph Drawing is to display hierarchical network structures as they appear in software engineering, project management and database design. The network is transformed into a directed acyclic graph that has to be drawn with edges that are strictly ....

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L. S. Heath and S. V. Pemmaraju. Stack and queue layouts of directed acyclic graphs: Part II. Technical report, Department of Computer Science, Virginia Polytechnic Institute & State University, july 1996.

Stack And Queue Layouts Of Directed Acyclic Graphs: Part II - Heath, Pemmaraju (1999) (16 citations) Self-citation (Heath Pemmaraju) (Correct)

....queue layout, book embedding, graph embedding, directed acyclic graphs, dags, graph algorithms, leveled planar graphs, NP complete, posets AMS subject classifications. 05C99, 68Q15, 68Q25, 68R10, 94C15 PII. S0097539795291550 Introduction. This is a companion paper to Heath, Pemmaraju, and Trenk [9]; we assume familiarity with the definitions, notation, and results in section 1 of that paper. There, we define stack and queue layouts of directed acyclic graphs (dags) and establish the stacknumber and queuenumber of path dags, cycle dags, tree dags, and unicyclic dags. We also provide a ....

....1 stack dag. Since its covering graph B is a 1 stack graph, B is outerplanar. Since B is biconnected and outerplanar, it contains a unique Hamiltonian cycle; call it C. Let # C be the dag that is a subgraph of # B and that has C as its covering graph. Clearly # C is a 1 stack dag. By Lemma 2. 2 of [9], # C contains a unique directed Hamiltonian path; say it is given by v 1 , v 2 , v n . As a dag can have at most one Hamiltonian path, this is also the unique Hamiltonian path in # B. Then # = v 1 , v 2 , v n is the unique topological order of # B that yields a 1 stack layout of ....

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L. S. Heath, S. V. Pemmaraju, and A. Trenk, Stack and queue layouts of directed acyclic graphs: Part I, SIAM J. Comput., (28 (1999), pp. 1510--1539.

Stack And Queue Layouts Of Posets - Heath, Pemmaraju (1997) (8 citations) Self-citation (Heath Pemmaraju) (Correct)

....that have been asked about stack and queue layouts of undirected graphs acquire a new flavor when there are directed edges (arcs) This is because the direction of the arcs imposes restrictions on the node orders that can be considered. Heath and Pemmaraju [9] and Heath, Pemmaraju, and Trenk [11, 12] initiate the study of stack and queue layouts of dags and provide optimal stack and queue layouts for several classes of dags. In this paper, we focus on stack and queue layouts of posets. Posets are ubiquitous mathematical objects, and various measures of their structure have been defined. Some ....

<F3.765e+05> L. S. Heath, S. V. Pemmaraju, and A.<F3.82e+05> Trenk,<F3.485e+05> Stack and queue layouts of directed acyclic graphs: Part<F3.82e+05> I, SIAM J. Comput. Sci., to appear.

Stack And Queue Layouts Of Posets - Heath, Pemmaraju (1997) (8 citations) Self-citation (Heath Pemmaraju) (Correct)

....with undirected graphs. Various questions that have been asked about stack and queue layouts of undirected graphs acquire a new flavor when there are directed edges (arcs) This is because the direction of the arcs imposes restrictions on the node orders that can be considered. Heath and Pemmaraju [9] and Heath, Pemmaraju, and Trenk [11, 12] initiate the study of stack and queue layouts of dags and provide optimal stack and queue layouts for several classes of dags. In this paper, we focus on stack and queue layouts of posets. Posets are ubiquitous mathematical objects, and various measures of ....

....that the queuenumber of a planar poset is within a small constant factor of its width. In section 5, we show that the stacknumber of the class of n element posets with planar covering graphs is #(n) In section 6, the decision problem of recognizing a 4 queue poset is defined; Heath and Pemmaraju [9] and Heath, Pemmaraju, and Trenk [11] show that the problem is NPcomplete. In section 7, we present several open questions and conjectures concerning stack and queue layouts of posets. 2. Definitions. This section contains the definitions of stack and queue layouts of undirected graphs, dags, and ....

[Article contains additional citation context not shown here]

<F3.765e+05> L. S. Heath and S. V.<F3.82e+05> Pemmaraju,<F3.485e+05> Stack and queue layouts of directed acyclic graphs: Part<F3.82e+05> II, SIAM J. Comput. Sci., to appear.

Stack And Queue Layouts Of Directed Acyclic Graphs: Part I - Heath, Pemmaraju, Trenk (1996) (16 citations) Self-citation (Heath Pemmaraju) (Correct)

....property of the undirected graph underlying a dag. In particular, we consider the property of the underlying undirected graph being a path, a cycle, a tree, or a unicyclic graph. We also give forbidden subgraph characterizations of 1 queue tree dags and 1 queue cycle dags. In the companion paper [5], we develop algorithmic results for stack and queue layouts of dags. In particular, we show that 1 stack and 1queue dags can be recognized in linear time, while the problems of recognizing 9 stack dags and 4 queue dags are both NP complete. The organization of this paper is as follows. Section 1 ....

L. S. Heath and S. V. Pemmaraju, Stack and queue layouts of directed acyclic graphs: Part II. Submitted, 1995. STACK AND QUEUE LAYOUTS OF DIRECTED ACYCLIC GRAPHS: PART I 39

Recognizing Leveled-Planar Dags in Linear Time - Heath, Pemmaraju (1996) (20 citations) Self-citation (Heath Pemmaraju) (Correct)

.... of the PQ tree data structure introduced by Booth and Lueker [2] One motivation for our algorithm is that it can be extended to recognize 1 queue dags, thus answering an open question in [6] Combinatorial and algorithmic results related to queue layouts of dags and posets can be found in [4, 7, 5]. Our algorithms also contrasts leveled planar undirected graphs and leveled planar dags, since the problem of recognizing leveled planar graphs has been shown to be NP complete by Heath and Rosenberg [8] Another motivation comes from the importance of the above problem in the area of graph ....

Lenwood S. Heath, Sriram V. Pemmaraju, and Ann Trenk. Stack and queue layouts of directed acyclic graphs: Part I. Technical Report 95-03, University of Iowa, 1995. Submitted.

Recognizing Leveled-Planar Dags in Linear Time - Heath, Pemmaraju (1996) (20 citations) Self-citation (Heath Pemmaraju) (Correct)

.... of the PQ tree data structure introduced by Booth and Lueker [2] One motivation for our algorithm is that it can be extended to recognize 1 queue dags, thus answering an open question in [6] Combinatorial and algorithmic results related to queue layouts of dags and posets can be found in [4, 7, 5]. Our algorithms also contrasts leveled planar undirected graphs and leveled planar dags, since the problem of recognizing leveled planar graphs has been shown to be NP complete by Heath and Rosenberg [8] Another motivation comes from the importance of the above problem in the area of graph ....

Lenwood S. Heath and Sriram V. Pemmaraju. Stack and queue layouts of directed acyclic graphs: Part II. Technical Report 95-06, University of Iowa, 1995. Submitted.

Radial Level Planarity Testing and Embedding in.. - Bachmaier.. (2004) (2 citations) (Correct)