{"id":164813,"date":"2013-05-24T00:00:00","date_gmt":"2013-05-24T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/the-symmetric-shortest-path-table-routing-conjecture\/"},"modified":"2018-10-16T20:39:23","modified_gmt":"2018-10-17T03:39:23","slug":"the-symmetric-shortest-path-table-routing-conjecture","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/the-symmetric-shortest-path-table-routing-conjecture\/","title":{"rendered":"The Symmetric Shortest-Path Table Routing Conjecture"},"content":{"rendered":"<div class=\"asset-content\">\n<p>A symmetric shortest-path table routing is a set of paths between all pairs of nodes in a graph such that the set is closed under path reversal, each path is a shortest path in the graph, and all paths with the same destination form a tree with a sink at the destination.  Such a routing can be found for any finite, connected, undirected, positive-weighted graph by \u201csalting\u201d the edge weights so that all the shortest salted paths are unique while each one remains a shortest path in the original graph.  A conjecture arises about whether every possible symmetric shortest-path table routing can be selected in this way by some edge weight salting.  It turns out that this conjecture is false.  This paper describes the search for counterexamples.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A symmetric shortest-path table routing is a set of paths between all pairs of nodes in a graph such that the set is closed under path reversal, each path is a shortest path in the graph, and all paths with the same destination form a tree with a sink at the destination. Such a routing [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"user_nicename","value":"tomr"}],"msr_publishername":"Microsoft Technical 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