Re: Should i use a hashmap?
HashMaps maps one key to one item. You can map the same item to multiple keys. However, in a HashMap all keys must be unique so you can't map multiple items to the same key. I don't see HashMaps helping you anymore than ArrayLists (on the contrary, they would be more cumbersome).
If you're allowed to change the the artist (or event) class, that would be the way to go. Simply add to the artist (or event) class any collection you like of events. By virtue, any event could turn up in different artist's collections of events, and an artist can contain multiple events.
Otherwise, you could look into using graphs. Simply define a graph which can contain both events and artists as nodes, then define edges which would link artists to their associated events and vise-versa. Technically such a graph layout could allow you to associate an artist with another artist, or an event with another event, but if you properly encapsulate your graph (and/or use it smartly) you can avoid this.
Re: Should i use a hashmap?