Topic
Bigraph
About: Bigraph is a research topic. Over the lifetime, 210 publications have been published within this topic receiving 2510 citations.
Papers published on a yearly basis
Papers
TL;DR: This letter reinterpret PDA from a new perspective, i.e., the strong edge coloring of bipartite graph (bigraph), and proves that, a PDA is equivalent to a strong edge colored bigraph.
Abstract: The technique of coded caching proposed by Madddah-Ali and Niesen is a promising approach to alleviate the load of networks during peak-traffic times. Recently, placement delivery array (PDA) was presented to characterize both the placement and delivery phase in a single array for the centralized coded caching algorithm. In this letter, we reinterpret PDA from a new perspective, i.e., the strong edge coloring of bipartite graph (bigraph). We prove that, a PDA is equivalent to a strong edge colored bigraph. Thus, we can construct a class of PDAs from existing structures in bigraphs. The class subsumes the scheme proposed by Maddah-Ali et al. and a more general class of PDAs proposed by Shangguan et al. as special cases.
187 citations
TL;DR: This paper axiomatises the structure ofbigraphs, and proves that the resulting theory is complete, because bigraphs treat locality and connectivity orthogonally.
Abstract: This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the $\pi$-calculus, mobile ambients and Petri nets in a way that is faithful to each of those models of discrete behaviour. While the main purpose of bigraphs is to understand mobile systems, a prerequisite for this understanding is a well-behaved theory of the structure of states in such systems. The algebra of bigraph structure is surprisingly simple, as this paper demonstrates; this is because bigraphs treat locality and connectivity orthogonally.
72 citations
TL;DR: This work defines bigraphs with sharing, which solves this problem by an extension of the basic formalism: the place graph is defined as a directed acyclic graph, thus allowing a natural representation of overlapping or intersecting locations.
57 citations
11 Jul 2005
TL;DR: This work introduces a general framework for logics whose terms represent arrows in monoidal categories and instantiates the framework to bigraphical structures and obtains a logic that is a natural composition of a place graph logic and a link graph logic.
Abstract: Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts.
56 citations
TL;DR: The interaction between this correspondence between bigraphs and digraphs determined by the utilization of the adjacency matrix and a theory of matrix decomposability that is developed in several different articles is explored.
Abstract: It was observed by Dulmage and Mendelsohn in their work on matrix reducibility that there is a one-to-one correspondence between bigraphs and digraphs determined by the utilization of the adjacency matrix. In this semiexpository paper we explore the interaction between this correspondence and a theory of matrix decomposability that is developed in several different articles. These results include: (a) a characterization of those bipartite graphs that can be labeled so that the resulting digraph is symmetric; (b) a criterion for the bigraph of a symmetric digraph to be connected; (c) a necessary and sufficient condition for a square binary matrix to be fully indecomposable in terms of its associated bigraph, and (d) matrix criteria for a digraph to be strongly, unilaterally, or weakly connected. We close with an unsolved extermal problem on the number of components of the bigraph of various orientations of a given graph. This leads to new amusing characterizations of trees and bigraphs.
Dedicated to the graph-theoretic partnership of Lloyd Dulmage and Nathan Mendelsohn.
55 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 14 |
| 2019 | 12 |
| 2018 | 10 |
| 2017 | 14 |
| 2016 | 19 |