Add ranking

Project.toml

@@ -1,7 +1,7 @@
 name = "Posets"
 uuid = "9a158a65-591e-4f68-ac4f-9ffef2fc51f2"
 authors = ["Ed Scheinerman <ers@jhu.edu>"]
-version = "0.3.1"
+version = "0.3.2"
 
 [deps]
 AbstractLattices = "398f06c4-4d28-53ec-89ca-5b2656b7603d"

README.md

@@ -254,15 +254,15 @@ However, the expression `p[a] < p[b]`  throws an error in either of these situat
 * Using the syntax `p[a]` if `a` is not an element of `p`.
 * Trying to compare elements of different posets (even if the two posets are equal).
 
-#### Comparability check
+### Comparability check
 
 The functions `are_comparable(p,a,b)` and `are_incomparable(p,a,b)` behave as follows:
 * `are_comparable(p,a,b)` returns `true` exactly when `a` and `b` are both in the poset, and one of the following is true: `a<b`, `a==b`, or `a>b`. 
 * `are_incompable(p,a,b)` returns `true` exactly when `a` and `b` are both in the poset, but none of the follower are true: `a<b`, `a==b`, or `a>b`.
 
 Alternatively, use `p[a] ⟂ p[b]` to test if `a` and `b` are comparable, and use `p[a] ∥ p[b]` to test if `a` and `b` are incomparable. 
 
-#### Chain/antichain check
+### Chain/antichain check
 
 Given a list of elements `vlist` of a poset `p`:
 
@@ -451,6 +451,16 @@ julia> dimension(p)
 
 > **Note**: Computation of the dimension of a poset is NP-hard. The `dimension` function may be slow, even for moderate-size posets.
 
+### Ranking
+
+The function `ranking(p)` returns a ranking (as a dictionary) of the poset 
+starting from the minimal elements.
+That is, the minimal elements are assigned rank 0. Elements that are above only elements of 
+rank 0 are assigned rank 1. Elements that are only above elements of rank 0 and 1 are assigned 
+rank 2. And so forth. 
+
+Note that not all posets are ranked, but this function always returns a result. 
+
 
 ## Standard Posets
 

docs/build/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-08-29T16:52:21","documenter_version":"1.5.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-08-31T15:16:50","documenter_version":"1.5.0"}}

docs/src/index.md

@@ -254,15 +254,15 @@ However, the expression `p[a] < p[b]`  throws an error in either of these situat
 * Using the syntax `p[a]` if `a` is not an element of `p`.
 * Trying to compare elements of different posets (even if the two posets are equal).
 
-#### Comparability check
+### Comparability check
 
 The functions `are_comparable(p,a,b)` and `are_incomparable(p,a,b)` behave as follows:
 * `are_comparable(p,a,b)` returns `true` exactly when `a` and `b` are both in the poset, and one of the following is true: `a<b`, `a==b`, or `a>b`. 
 * `are_incompable(p,a,b)` returns `true` exactly when `a` and `b` are both in the poset, but none of the follower are true: `a<b`, `a==b`, or `a>b`.
 
 Alternatively, use `p[a] ⟂ p[b]` to test if `a` and `b` are comparable, and use `p[a] ∥ p[b]` to test if `a` and `b` are incomparable. 
 
-#### Chain/antichain check
+### Chain/antichain check
 
 Given a list of elements `vlist` of a poset `p`:
 
@@ -451,6 +451,16 @@ julia> dimension(p)
 
 > **Note**: Computation of the dimension of a poset is NP-hard. The `dimension` function may be slow, even for moderate-size posets.
 
+### Ranking
+
+The function `ranking(p)` returns a ranking (as a dictionary) of the poset 
+starting from the minimal elements.
+That is, the minimal elements are assigned rank 0. Elements that are above only elements of 
+rank 0 are assigned rank 1. Elements that are only above elements of rank 0 and 1 are assigned 
+rank 2. And so forth. 
+
+Note that not all posets are ranked, but this function always returns a result. 
+
 
 ## Standard Posets
 

src/Posets.jl

@@ -96,6 +96,7 @@ export Poset,
     nv,
     random_linear_order,
     random_poset,
+    ranking,
     realizer,
     relations,
     rem_relation!,

src/up-down.jl

@@ -24,3 +24,31 @@ Return an iterator for all elements `k` such that `a < k < b`.
 function between(p::Poset, a::Integer, b::Integer)
     return (k for k in 1:nv(p) if p(a, k) && p(k, b))
 end
+
+"""
+    ranking(p::Poset)::Dict{Int,Int}
+
+Create a ranking of the poset `p`. This is a dictionary that 
+gives a ranking for each element of `p`. Minimals have rank 0.
+Elements that are over only minimals have grade 1. And so forth. 
+"""
+function ranking(p::Poset)::Dict{Int,Int}
+    n = nv(p)
+    gr = Dict{Int,Int}()
+    for v in 1:n
+        gr[v] = 0
+    end
+    done = Set{Int}()
+    todo = Set{Int}(1:n)
+    g = -1
+    while length(todo) > 0
+        g += 1
+        next = [v for v in todo if below(p, v) ⊆ done]
+        for x in next
+            gr[x] = g
+            delete!(todo, x)
+            push!(done, x)
+        end
+    end
+    return gr
+end

test/runtests.jl

@@ -134,6 +134,11 @@ end
     q = random_poset(5)
     iso(p * q, q * p)
     @test nv(p * q) == nv(p) * nv(q)
+
+    p = subset_lattice(4)
+    r = ranking(p)
+    mids = [v for v in 1:nv(p) if r[v] == 2]
+    @test length(mids) == binomial(4, 2)
 end
 
 @testset "Connection" begin