I've been trying for a while now to implement a Dijkstra shortest path algorithm in JIProlog. There are a few implementations available online, such as here and here, but they all return the path as a list of nodes. This is problematic for my implementation, because I'm technically using a multigraph, where vertices can be connected by multiple edges. Therefore, I need an algorithm that returns a list of edges rather than a list of nodes.
I've been trying to adjust the first implementation I mentioned to track edges, but I get lost in the dijkstra_l/3 rule. Could someone help me? Thanks!
I answered some time ago to a similar question, with an implementation. Alas, that code doesn't work with the lastes SWI-Prlog, I've debugged and found that ord_memberchk (used for efficiency) has changed behaviour. I've replaced with memberchk and now is working...
I would suggest to use the output of the algorithm with a simple post processing pass that recovers the edges from nodes, selecting the smaller value. I've implemented as it dijkstra_edges/3
/* File: dijkstra_av.pl
Author: Carlo,,,
Created: Aug 3 2012
Modified:Oct 28 2012
Purpose: learn graph programming with attribute variables
*/
:- module(dijkstra_av, [dijkstra_av/3,
dijkstra_edges/3]).
dijkstra_av(Graph, Start, Solution) :-
setof(X, Y^D^(member(d(X,Y,D), Graph) ; member(d(Y,X,D), Graph)), Xs),
length(Xs, L),
length(Vs, L),
aggregate_all(sum(D), member(d(_, _, D), Graph), Infinity),
catch((algo(Graph, Infinity, Xs, Vs, Start, Solution),
throw(sol(Solution))
), sol(Solution), true).
dijkstra_edges(Graph, Start, Edges) :-
dijkstra_av(Graph, Start, Solution),
maplist(nodes_to_edges(Graph), Solution, Edges).
nodes_to_edges(Graph, s(Node, Dist, Nodes), s(Node, Dist, Edges)) :-
join_nodes(Graph, Nodes, Edges).
join_nodes(_Graph, [_Last], []).
join_nodes(Graph, [N,M|Ns], [e(N,M,D)|Es]) :-
aggregate_all(min(X), member(d(N, M, X), Graph), D),
join_nodes(Graph, [M|Ns], Es).
algo(Graph, Infinity, Xs, Vs, Start, Solution) :-
pairs_keys_values(Ps, Xs, Vs),
maplist(init_adjs(Ps), Graph),
maplist(init_dist(Infinity), Ps),
%ord_memberchk(Start-Sv, Ps),
memberchk(Start-Sv, Ps),
put_attr(Sv, dist, 0),
time(main_loop(Vs)),
maplist(solution(Start), Vs, Solution).
solution(Start, V, s(N, D, [Start|P])) :-
get_attr(V, name, N),
get_attr(V, dist, D),
rpath(V, [], P).
rpath(V, X, P) :-
get_attr(V, name, N),
( get_attr(V, previous, Q)
-> rpath(Q, [N|X], P)
; P = X
).
init_dist(Infinity, N-V) :-
put_attr(V, name, N),
put_attr(V, dist, Infinity).
init_adjs(Ps, d(X, Y, D)) :-
%ord_memberchk(X-Xv, Ps),
%ord_memberchk(Y-Yv, Ps),
memberchk(X-Xv, Ps),
memberchk(Y-Yv, Ps),
adj_add(Xv, Yv, D),
adj_add(Yv, Xv, D).
adj_add(X, Y, D) :-
( get_attr(X, adjs, L)
-> put_attr(X, adjs, [Y-D|L])
; put_attr(X, adjs, [Y-D])
).
main_loop([]).
main_loop([Q|Qs]) :-
smallest_distance(Qs, Q, U, Qn),
put_attr(U, assigned, true),
get_attr(U, adjs, As),
update_neighbours(As, U),
main_loop(Qn).
smallest_distance([A|Qs], C, M, [T|Qn]) :-
get_attr(A, dist, Av),
get_attr(C, dist, Cv),
( Av < Cv
-> (N,T) = (A,C)
; (N,T) = (C,A)
),
!, smallest_distance(Qs, N, M, Qn).
smallest_distance([], U, U, []).
update_neighbours([V-Duv|Vs], U) :-
( get_attr(V, assigned, true)
-> true
; get_attr(U, dist, Du),
get_attr(V, dist, Dv),
Alt is Du + Duv,
( Alt < Dv
-> put_attr(V, dist, Alt),
put_attr(V, previous, U)
; true
)
),
update_neighbours(Vs, U).
update_neighbours([], _).
:- begin_tests(dijkstra_av).
small([d(a,b,2),d(a,b,1),d(b,c,1),d(c,d,1),d(a,d,3),d(a,d,2)]).
test(1) :-
nl,
small(S),
time(dijkstra_av(S, a, L)),
maplist(writeln, L).
test(2) :-
open('salesman.pl', read, F),
readf(F, L),
close(F),
nl,
dijkstra_av(L, penzance, R),
maplist(writeln, R).
readf(F, [d(X,Y,D)|R]) :-
read(F, dist(X,Y,D)), !, readf(F, R).
readf(_, []).
test(3) :-
nl, small(S),
time(dijkstra_edges(S, a, Es)),
maplist(writeln, Es).
:- end_tests(dijkstra_av).
test(3) shows the implementation, I've added some edge with higher values to verify, the output shows that these are correctly discarded:
s(a,0,[])
s(b,1,[e(a,b,1)])
s(c,2,[e(a,b,1),e(b,c,1)])
s(d,2,[e(a,d,2)])