Dijkstra's algorithm using heap

One can store an array of pointers, one for each node, that points to the location of that vertex in the heap used in Dijkstra's algorithm. When each heap operation is applied (e.g. the removal of the top element), one can easily update this array for each swap operation in memory that is thus made. (So one can define a modified heap data structure such that each element in the heap has a key (i.e. a pointer), and one can immediately find the element in the heap for a given key, even if the heap changes.) This way, if you want to look up a node in the heap, you don't need to do a linear search, but just check the pointer for that node.