This is a great quesion! There is lot of work still being done on this. Unfortunately I don't think I know enough about CS or computer engineering to make analogies, so I'll give a quick crash course and some examples instead and hope you find it helpful. Long story short though is that we are just now making really exciting headway into how memory might actually be stored and recalled and its usually a very dynamic, active, and possibly even stochastic process, not really like a search algorithm in a computer at all.
The brain works differently than a computer in that it encodes all of its information in frequency of signal firing and the patterns of firing between circuits with varying stregnths of connections based on experiences. Frequency is dependent on the neuron itself and patterns of firing between circuits are dependent on where the neurons project to, and how strongly they interact with the next neuron. At this very basic level memory is stored and recalled by placing proteins in the membranes of neurons that are strongly activated to make them easier activated in the future. These are sort of the first steps toward memory. This is called long term potentiation and just means that this neuron is primed to fire more readily and stronger in response to similar input in the future.
To build on this, there is a classic example of this occuring and causing sensitization ( an exaggerated response to the same stimulus) in conditioning experiments in the sea slug Aplysia. Aplysia has a reflex where it will withdraw its gills slightly if you touch its siphon. You can pair a shock to the tail (unconditioned stimulus) which elicits a large withdrawal of the gills, with a conditioned stimulus (touching its syphon to elicit the withdrawal reflex) to get the sea slug to associate the two. The end result is that the sea slug will learn/"remember" to withdraw its gills fully in the presence of the syphon touch. No learning cannot happen without recall of some sort, and in this example the slug was associating and learning from two "circuits" to produce a different behavior.
In something a little more complex than a slug, memory and recall still functions much the same way, its just the circuits that are interacting are entire brain regions. Most people view the hippocampus as acting sort of like a relay center and boot loader for different memories by taking external input and sorting them to the right parts of the brain. A good example of this would be the difference between dorsal and ventral streams of information in the brain. For a really basic breakdown of this phenomenon there are two areas of your brain that I will focus on - the parietal lobe and the temporal lobe. The parietal lobe is known to be involved in spatial processing, and the temporal lobes are known to be involved in semantic and auditory processing. When information enters the brain (eyes, ears, nose etc.) it will be processed by sensory structures, sent to the thalamus and hippocampus to be "relayed" to the right areas of the brain. Relayed in this case is going to be dictated by whatever connections and how strong they are in the brain. In this case from proteins expressed in the cellular membrane that make some neurons in the hippocampus more responsive than others, so they are more likely to fire. Then, it depends on where they are projecting to that determines where they information is sent.
It just so happens the brain is arranged in such a way that neurons projecting dorsally, or to the parietal lobe I mentioned, will tell you "where" the stimulus is, and those projecting ventral to the temporal lobes will tell you "what" it is. This is achieved because these lobes are highly interconnected to even more regions in the brain and send their processed "where" and "what" info as input to other regions. These regions will all fire a certain way in response to this information and that pattern of firing can be considered a recollection or memory. Sorry that this is dense and so crash course-y but I hope it is helpful in clarifying how the brain recalls some information. Of course this is a developing field and we are learning more about how it functions every day. These are just some classic examples.