65536553
65546554
65556555
6556+
6557+
65566558
65576559
65586560
65656567
65666568
65676569
6570+
6571+
65686572
65696573
65706574
65716575
65726576
65736577
6574-
6578+
6579+
6580+
65756581
65766582
65776583
66056611
66066612
66076613
6614+
6615+
6616+
6617+
66086618
66096619
66106620
66176627< ul class ="metadata page-metadata " data-bi-name ="page info " lang ="en-us " dir ="ltr ">
66186628
66196629 Last update:
6620- < span class ="git-revision-date-localized-plugin git-revision-date-localized-plugin-date " title ="May 2 , 2025 18:37:17 UTC> May 2 , 2025</ span >  
6630+ < span class ="git-revision-date-localized-plugin git-revision-date-localized-plugin-date " title ="June 14 , 2025 10:11:52 UTC> June 14 , 2025</ span >  
66216631
66226632<!-- Tags -->
66236633
@@ -6683,7 +6693,7 @@ <h2 id="shortest-paths-of-a-fixed-length">Shortest paths of a fixed length<a cla
66836693Then the following formula computes each entry of < span class ="arithmatex "> $L_{k+1}$</ span > :</ p >
66846694< div class ="arithmatex "> $$L_{k+1}[i][j] = \min_{p = 1 \ldots n} \left(L_k[i][p] + G[p][j]\right)$$</ div >
66856695< p > When looking closer at this formula, we can draw an analogy with the matrix multiplication:
6686- in fact the matrix < span class ="arithmatex "> $L_k$</ span > is multiplied by the matrix < span class ="arithmatex "> $G$</ span > , the only difference is that instead in the multiplication operation we take the minimum instead of the sum.</ p >
6696+ in fact the matrix < span class ="arithmatex "> $L_k$</ span > is multiplied by the matrix < span class ="arithmatex "> $G$</ span > , the only difference is that instead in the multiplication operation we take the minimum instead of the sum, and the sum instead of the multiplication as the inner operation .</ p >
66876697< div class ="arithmatex "> $$L_{k+1} = L_k \odot G,$$</ div >
66886698< p > where the operation < span class ="arithmatex "> $\odot$</ span > is defined as follows:</ p >
66896699< div class ="arithmatex "> $$A \odot B = C~~\Longleftrightarrow~~C_{i j} = \min_{p = 1 \ldots n}\left(A_{i p} + B_{p j}\right)$$</ div >
@@ -6703,7 +6713,7 @@ <h2 id="generalization-of-the-problems-for-paths-with-length-up-to-k">Generaliza
67036713
67046714< ul class ="metadata page-metadata " data-bi-name ="page info " lang ="en-us " dir ="ltr ">
67056715 < span class ="contributors-text "> Contributors:</ span >
6706- < ul class ="contributors " data-bi-name ="contributors "> < li > < a href ="https://github.com/jakobkogler " title ="jakobkogler " data-bi-name ="contributorprofile " target ="_blank "> jakobkogler</ a > (91.4 %)</ li > < li > < a href ="https://github.com/adamant-pwn " title ="adamant-pwn " data-bi-name ="contributorprofile " target ="_blank "> adamant-pwn</ a > (6.45 %)</ li > < li > < a href ="https://github.com/bit-shashank " title ="bit-shashank " data-bi-name ="contributorprofile " target ="_blank "> bit-shashank</ a > (1.08%)</ li > < li > < a href ="https://github.com/wikku " title ="wikku " data-bi-name ="contributorprofile " target ="_blank "> wikku</ a > (1.08%)</ li > </ ul >
6716+ < ul class ="contributors " data-bi-name ="contributors "> < li > < a href ="https://github.com/jakobkogler " title ="jakobkogler " data-bi-name ="contributorprofile " target ="_blank "> jakobkogler</ a > (90.32 %)</ li > < li > < a href ="https://github.com/adamant-pwn " title ="adamant-pwn " data-bi-name ="contributorprofile " target ="_blank "> adamant-pwn</ a > (7.53 %)</ li > < li > < a href ="https://github.com/bit-shashank " title ="bit-shashank " data-bi-name ="contributorprofile " target ="_blank "> bit-shashank</ a > (1.08%)</ li > < li > < a href ="https://github.com/wikku " title ="wikku " data-bi-name ="contributorprofile " target ="_blank "> wikku</ a > (1.08%)</ li > </ ul >
67076717</ ul >
67086718
67096719 </ article >
0 commit comments