
TL;DR
This paper introduces the concept of edge-orders, a unifying framework for edge-connectivity analogous to vertex-based canonical orderings, and provides linear-time algorithms for constructing edge-independent spanning trees.
Contribution
It establishes the first edge-order concepts for edge-connectivity and develops linear-time algorithms for their computation, improving existing methods for spanning tree construction.
Findings
Linear-time algorithms for (1,1)-edge-orders and (2,1)-edge-orders.
Construction of edge-independent spanning trees in linear time.
Improved algorithms for the Edge-Independent Spanning Tree Conjecture.
Abstract
Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying concept behind all these orders has been shown: they can be described by a graph decomposition into parts that have a prescribed vertex-connectivity. Despite extensive interest in canonical orderings, no analogue of this unifying concept is known for edge-connectivity. In this paper, we establish such a concept named edge-orders and show how to compute (1,1)-edge-orders of 2-edge-connected graphs as well as (2,1)-edge-orders of 3-edge-connected graphs in linear time, respectively. While the former can be seen as the edge-variants of st-numberings, the latter are the edge-variants of Mondshein sequences and non-separating ear decompositions. The methods that we use for obtaining such edge-orders differ considerably in almost…
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Taxonomy
TopicsInterconnection Networks and Systems · Advanced Graph Theory Research · Complexity and Algorithms in Graphs
