How can I find journals in my field that do not charge author fees?
You can use websites like DOAJ.org to search for relevant open access journals that do not charge publication fees. 

This example query for 'algorithms' reveals 40 such cost-free open access journals, some of which may be relevant to you, depending on what exact type of algorithm you're publishing.

Using this I found The Electronic Journal of Combinatorics &amp; Image Processing Online (IPOL Journal) which both look like reputable, high-quality, publication-fee-free, algorithm-relevant journals to me.

Some of the information is a little out of date though, for instance the journal Algorithms (MDPI) I think now charges 300 CHF (Swiss Francs) although initially it was free, in the past.