I found a solution for minimum hitting set on github: https://github.com/bdesham/hitting-set and then tried to use it. The solution is clojure library so I downloaded leiningen to try to run it.
I read the readme file from github link but I still didn't know how to run the clj code to get result of minimal hitting set. I saw that there was a function called minimal-hitting-sets in hitting_set.clj file but I don't know how to call it with argument. Eg: Get minimal hitting set of:
{"Australia" #{:white :red :blue},
"Tanzania" #{:black :blue :green :yellow},
"Norway" #{:white :red :blue},
"Uruguay" #{:white :blue :yellow},
"Saint Vincent and the Grenadines" #{:blue :green :yellow},
"Ivory Coast" #{:white :orange :green},
"Sierra Leone" #{:white :blue :green},
"United States" #{:white :red :blue}}
Project.clj code:
(defproject hitting-set "0.9.0"
:description "Find minimal hitting sets"
:url "https://github.com/bdesham/hitting-set"
:license {:name "Eclipse Public License"
:url "http://www.eclipse.org/legal/epl-v10.html"
:distribution :repo
:comments "Same as Clojure"}
:main hitting-set
:min-lein-version "2.0.0"
:dependencies [ [org.clojure/clojure "1.4.0"]
[hitting-set "0.9.0"]])hitting_set.clj code:
(ns hitting-set
(:use hitting-set :only [minimal-hitting-sets]))
; Utility functions
(defn- dissoc-elements-containing
"Given a map in which the keys are sets, removes all keys whose sets contain
the element el. Adapted from http://stackoverflow.com/a/2753997/371228"
[el m]
(apply dissoc m (keep #(-> % val
(not-any? #{el})
(if nil (key %)))
m)))
(defn- map-old-new
"Returns a sequence of vectors. Each first item is an element of coll and the
second item is the result of calling f with that item."
[f coll]
(map #(vector % (f %)) coll))
(defn- count-vertices
"Returns the number of vertices in the hypergraph h."
[h]
(count (apply union (vals h))))
(defn- sorted-hypergraph
"Returns a version of the hypergraph h that is sorted so that the edges with
the fewest vertices come first."
[h]
(into (sorted-map-by (fn [key1 key2]
(compare [(count (get h key1)) key1]
[(count (get h key2)) key2])))
h))
(defn- remove-dupes
"Given a map m, remove all but one of the keys that map to any given value."
[m]
(loop [sm (sorted-map),
m m,
seen #{}]
(if-let [head (first m)]
(if (contains? seen (second head))
(recur sm
(rest m)
seen)
(recur (assoc sm (first head) (second head))
(rest m)
(conj seen (second head))))
sm)))
(defn- efficient-hypergraph
"Given a hypergraph h, returns an equivalent hypergraph that will go through
the hitting set algorithm more quickly. Specifically, redundant edges are
discarded and then the map is sorted so that the smallest edges come first."
[h]
(-> h remove-dupes sorted-hypergraph))
(defn- largest-edge
"Returns the name of the edge of h that has the greatest number of vertices."
[h]
(first (last (sorted-hypergraph h))))
(defn- remove-vertices
"Given a hypergraph h and a set vv of vertices, remove the vertices from h
(i.e. remove all of the vertices of vv from each edge in h). If this would
result in an edge becoming empty, remove that edge entirely."
[h vv]
(loop [h h,
res {}]
(if (first h)
(let [edge (difference (second (first h))
vv)]
(if (< 0 (count edge))
(recur (rest h)
(assoc res (first (first h)) edge))
(recur (rest h)
res)))
res)))
; Auxiliary functions
;
; These functions might be useful if you're working with hitting sets, although
; they're not actually invoked anywhere else in this project.
(defn reverse-map
"Takes a map from keys to sets of values. Produces a map in which the values
are mapped to the set of keys in whose sets they originally appeared."
[m]
(apply merge-with into
(for [[k vs] m]
(apply hash-map (flatten (for [v vs]
[v #{k}]))))))
(defn drop-elements
"Given a set of N elements, return a set of N sets, each of which is the
result of removing a different item from the original set."
[s]
(set (for [e s] (difference s #{e}))))
; The main functions
;
; These are the functions that users are probably going to be interested in.
; Hitting set
(defn hitting-set?
"Returns true if t is a hitting set of h. Does not check whether s is
minimal."
[h t]
(not-any? empty? (map #(intersection % t)
(vals h))))
(defn hitting-set-exists?
"Returns true if a hitting set of size k exists for the hypergraph h. See the
caveat in README.md for odd behavior of this function."
[h k]
(cond
(< (count-vertices h) k) false
(empty? h) true
(zero? k) false
:else (let [hvs (map #(dissoc-elements-containing % h)
(first (vals h)))]
(boolean (some #(hitting-set-exists? % (dec k))
hvs)))))
(defn- enumerate-algorithm
[h k x]
(cond
(empty? h) #{x}
(zero? k) #{}
:else (let [hvs (map-old-new #(dissoc-elements-containing % h)
(first (vals h)))]
(apply union (map #(enumerate-algorithm (second %)
(dec k)
(union x #{(first %)}))
hvs)))))
(defn enumerate-hitting-sets
"Return a set containing the hitting sets of h. See the caveat in README.md
for odd behavior of this function. If the parameter k is passed then the
function will return all hitting sets of size less than or equal to k."
([h]
(enumerate-algorithm (efficient-hypergraph h) (count-vertices h) #{}))
([h k]
(enumerate-algorithm (efficient-hypergraph h) k #{})))
(defn minimal-hitting-sets
"Returns a set containing the minimal hitting sets of the hypergraph h. If
you just want one hitting set and don't care whether there are multiple
minimal hitting sets, use (first (minimal-hitting-sets h))."
[h]
(first (filter #(> (count %) 0)
(map #(enumerate-hitting-sets h %)
(range 1 (inc (count-vertices h)))))))
; Set cover
(defn cover?
"Returns true if the elements of s form a set cover for the hypergraph h."
[h s]
(= (apply union (vals h))
(apply union (map #(get h %) s))))
(defn greedy-cover
"Returns a set cover of h using the 'greedy' algorithm."
[h]
(loop [hh h,
edges #{}]
(if (cover? h edges)
edges
(let [e (largest-edge hh)]
(recur (remove-vertices hh (get hh e))
(conj edges e))))))
(defn approx-hitting-set
"Returns a hitting set of h. The set is guaranteed to be a hitting set, but
may not be minimal."
[h]
(greedy-cover (reverse-map h)))Since I am a new bie to leiningen and clojure so I really need your help on it.
Thanks, Hung
