The path set polytope of an acyclic, directed graph with an application to machine sequencing

Networks ◽  
1989 ◽  
Vol 19 (5) ◽  
pp. 607-614 ◽  
Author(s):  
John H. Vande Vate
Keyword(s):  
Directed Graph ◽  
Acyclic Directed Graph

scholarly journals The structure of intrinsic complexity of learning

1997 ◽  
Vol 62 (4) ◽  
pp. 1187-1201 ◽  
Author(s):  
Sanjay Jain ◽  
Arun Sharma
Keyword(s):  
Directed Graph ◽  
Learning Algorithm ◽  
Recursion Theory ◽  
Language Identification ◽  
Learning Problems ◽  
Pattern Languages ◽  
Language Classes ◽  
Resource Requirements ◽  
Intrinsic Complexity ◽  
Acyclic Directed Graph

AbstractLimiting identification of r.e. indexes for r.e. languages (from a presentation of elements of the language) and limiting identification of programs for computable functions (from a graph of the function) have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of “intrinsic” complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursion theory to compare and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, Kinber, and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification.The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages.Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open.

scholarly journals Building a Chinese AMR Bank with Concept and Relation Alignments

2019 ◽  
Vol 18 (1) ◽  
Author(s):  
Bin Li ◽  
Yuan Wen ◽  
Li Song ◽  
Weiguang Qu ◽  
Nianwen Xue
Keyword(s):  
Quantitative Analysis ◽  
Directed Graph ◽  
Annotation Tool ◽  
Systematic Treatment ◽  
Tree Graphs ◽  
Discourse Relations ◽  
Significant Change ◽  
Meaning Representation ◽  
Acyclic Directed Graph

Abstract Meaning Representation (AMR) is a meaning representation framework in which the meaning of a full sentence is represented as a single-rooted, acyclic, directed graph. In this article, we describe an on-going project to build a Chinese AMR (CAMR) corpus, which currently includes 10,149 sentences from the newsgroup and weblog portion of the Chinese TreeBank (CTB). We describe the annotation specifications for the CAMR corpus, which follow the annotation principles of English AMR but make adaptations where needed to accommodate the linguistic facts of Chinese. The CAMR specifications also include a systematic treatment of sentence-internal discourse relations. One significant change we have made to the AMR annotation methodology is the inclusion of the alignment between word tokens in the sentence and the concepts/relations in the CAMR annotation to make it easier for automatic parsers to model the correspondence between a sentence and its meaning representation. We develop an annotation tool for CAMR, and the inter-agreement as measured by the Smatch score between the two annotators is 0.83, indicating reliable annotation. We also present some quantitative analysis of the CAMR corpus. 46.71% of the AMRs of the sentences are non-tree graphs. Moreover, the AMR of 88.95% of the sentences has concepts inferred from the context of the sentence but do not correspond to a specific word.

scholarly journals Coherent fans in the space of flows in framed graphs

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Vladimir I. Danilov ◽  
Alexander V. Karzanov ◽  
Gleb A. Koshevoy
Keyword(s):  
Simplicial Complex ◽  
Binary Relation ◽  
Directed Graph ◽  
The Other ◽  
Cluster Algebras ◽  
Linear Orders ◽  
International Audience ◽  
Acyclic Directed Graph ◽  
Extreme Rays ◽  
Space Of Flows

International audience Let $G=(V,E)$ be a finite acyclic directed graph. Being motivated by a study of certain aspects of cluster algebras, we are interested in a class of triangulations of the cone of non-negative flows in $G, \mathcal F_+(G)$. To construct a triangulation, we fix a raming at each inner vertex $v$ of $G$, which consists of two linear orders: one on the set of incoming edges, and the other on the set of outgoing edges of $v$. A digraph $G$ endowed with a framing at each inner vertex is called $framed$. Given a framing on $G$, we define a reflexive and symmetric binary relation on the set of extreme rays of $\mathcal F_+ (G)$. We prove that that the complex of cliques formed by this binary relation is a pure simplicial complex, and that the cones spanned by cliques constitute a unimodular simplicial regular fan $Σ (G)$ covering the entire $\mathcal F_+(G)$. Soit $G=(V,E)$ un graphe orientè, fini et acyclique. Nous nous intéressons, en lien avec l’étude de certains aspects des algèbres amassées, à une classe de triangulations du cône des flots positifs de $G, \mathcal F_+(G)$. Pour construire une triangulation, nous ajoutons une structure en chaque sommet interne $v$ de $G$, constituée de deux ordres totaux : l'un sur l'ensemble des arcs entrants, l'autre sur l'ensemble des arcs sortants de $v$. On dit alors que $G$ est structurè. On définit ensuite une relation binaire réflexive et symétrique sur l'ensemble des rayons extrêmes de $\mathcal F_+ (G)$. Nous démontrons que le complexe des cliques formè par cette relation binaire est un complexe simplicial pur, et que le cône engendré par les cliques forme un éventail régulier simplicial unimodulaire $Σ (G)$ qui couvre complètement $\mathcal F_+(G)$.

Acyclic Directed Graph

2008 ◽  
pp. 11-11
Author(s):  
Shashi Shekhar ◽  
Hui Xiong
Keyword(s):  
Directed Graph ◽  
Acyclic Directed Graph

A Minimax Equality Related to the Longest Directed Path in an Acyclic Graph

1975 ◽  
Vol 27 (2) ◽  
pp. 348-351 ◽  
Author(s):  
K. Vidyasankar ◽  
D. H. Younger
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Directed Path ◽  
Acyclic Graph ◽  
Vertex Set ◽  
Acyclic Directed Graph

As an analog of a recently established minimax equality for directed graphs [1], I. Simon has suggested that the following be investigated.1.1. For a finite acyclic directed graph G, a minimum collection of directed coboundaries whose union is the edge set of G has cardinality equal to that of a maximum strong matching of G.This minimax equality is here proved, using a characterization of a maximum strong matching of an acyclic graph as the set of edges of a longest directed path in the graph.The terms employed in the above theorem are defined as follows. Let G be a finite directed graph with vertex set VG and edge set eG

scholarly journals Cyclic inclusion-exclusion and the kernel of P -partitions

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Valentin Féray
Keyword(s):  
Directed Graph ◽  
Symmetric Function ◽  
Bipartite Graphs ◽  
Linear Map ◽  
Generating Series ◽  
International Audience ◽  
Decreasing Functions ◽  
Acyclic Directed Graph

International audience Following the lead of Stanley and Gessel, we consider a linear map which associates to an acyclic directed graph (or a poset) a quasi-symmetric function. The latter is naturally defined as multivariate generating series of non-decreasing functions on the graph (or of P -partitions of the poset).We describe the kernel of this linear map, using a simple combinatorial operation that we call cyclic inclusion- exclusion. Our result also holds for the natural non-commutative analog and for the commutative and non-commutative restrictions to bipartite graphs.

scholarly journals Replacement of Directed Graph by Acyclic Directed Graph and Its Application in Biostatistics

2018 ◽  
Vol 09 (02) ◽  
Author(s):  
Tsitsiashvili Gurami ◽  
Bulgakov Victor ◽  
Losev Alexandr
Keyword(s):  
Directed Graph ◽  
Acyclic Directed Graph
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