I doubt there's "an algorithm" for what you want to do. At least nothing more specific than, "Get the data you want into a structure and display it." In the first place, it'll depend on how the data is stored: by game, by player, some other way?

To visualize the timelines of the players focused on a particular game, my first thought is something like a candlestick graph that extends above and below a line representing the current game, where you can see how many games before and after this one a player was in. But whether that's a good choice would depend on how often players change. If players often play a single game and leave again, that'd be a pretty useless graph.

Thanks. That is a very useful direction. I am looking for some sort of flow with game number (on X axis) and Players on Y axis such that I can see a subset of N players played in window W of total games G ( For example: Games in current Year). I am developing more ideas.

Okay, if a 2-D chart of games to players will work, see what you think of this. The subroutine will handle any number of players, games, and players/game, as long as there are always the same number of players like you mentioned, and it displays a simple ASCII chart of a window between two numbered games. There's no error checking, and the formatting could get messed up with long names, but I think it does the basics.

#!/usr/bin/env perl
use 5.010; use warnings; use strict;
use List::Util qw(max first);

my @players = qw( Adam Bob Clay Dan Ed Frank George );
my @games = ( [1,2,3,4],
              [2,3,4,5],
              [2,4,5,6],
              [2,4,6,7],
              [2,4,6,7],
              [3,4,6,7],
              [1,3,4,7] );

chart( \@players, \@games, 2, 4 ); # print a chart from game 2 to 4
chart( \@players, \@games, 1, 7 ); # print a chart of all 7 games

sub chart {
    my $players = shift; # players array
    my $games   = shift; # games array
    my $start   = shift; # start game
    my $end     = shift; # end game
    my $pl      = max map { length $_ } @$players;

    say '-' x 40;
    for my $p ( 1..@$players ){
        printf "%-${pl}s | ", $players->[$p-1];
        for( $start..$end ){
            print is_in($p,$games->[$_-1]) ? 'X  ' : '   ';
        }
        say '';
    }
    say '-' x 40;
    printf "%-${pl}s | ", ' ';
    print "$_  " for $start..$end;
    say '';
}

sub is_in {
    return first { $_ == $_[0] } @{$_[1]};
}
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Aaron B.
Available for small or large Perl jobs and *nix system administration; see my home node.