Results 1 
1 of
1
A Brief History of Strahler Numbers
 In Language and Automata Theory and Applications
, 2014
"... Abstract. The Strahler number or HortonStrahler number of a tree, originally introduced in geophysics, has a surprisingly rich theory. We sketch some milestones in its history, and its connection to arithmetic expressions, graph traversing, decision problems for contextfree languages, Parikh’s th ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract. The Strahler number or HortonStrahler number of a tree, originally introduced in geophysics, has a surprisingly rich theory. We sketch some milestones in its history, and its connection to arithmetic expressions, graph traversing, decision problems for contextfree languages, Parikh’s theorem, and Newton’s procedure for approximating zeros of differentiable functions. 1 The Strahler Number In 1945, the geophysicist Robert Horton found it useful to associate a stream order to a system of rivers (geophysicists seem to prefer the term ‘stream”) [20]. Unbranched fingertip tributaries are always designated as of order 1, tributaries or streams of the 2d order receive branches or tributaries of the 1st order, but these only; a 3d order stream must receive one or more tributaries of the 2d order but may also receive 1st order tributaries. A 4th order stream receives branches of the 3d and usually also of lower orders, and so on. Several years later, Arthur N. Strahler replaced this ambiguous definition by a simpler one, very easy to compute [26]: The smallest, or ”fingertip”, channels constitute the firstorder segments. [...]. A secondorder segment is formed by the junction of any two firstorder streams; a thirdorder segment is formed by the joining of any two second order streams, etc. Streams of lower order joining a higher order stream do not change the order of the higher stream. Thus, if a firstorder stream joins a secondorder stream, it remains a secondorder stream. Figure 1 shows the Strahler number for a fragment of the course of the Elbe river with some of its tributaries. The stream system is of order 4. From a computer science point of view, stream systems are just trees. Definition 1. Let t be a tree with root r. The Strahler number of t, denoted by S(t), is inductively defined as follows. – If r has no children (i.e., t has only one node), then S(t) = 0.