However to answer the post you would need to define (or point us in the direction of) the "particular relation" you have in mind.

The particular relation where x is the future algorithm and y is the algorithm which characterizes me now is " x is psychologically continuous with y". If x contains memories of y's experiences, or if x contains memories of the experiences of intervening algorithms which in turn contain memories of y, or if x and y are linked by any series of algorithms connected in this way we would have good reason to think x is psychologically continuous with y. Though memory connections aren't sufficient,- you'd also want beliefs, values and emotions to persist or not persist in the right way.

Of course, death is rather flexible. There is no fact of the matter about how continuous with you an algorithm has to be for it to count as you dying.