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Taking notes, I was going to write this:
therefore p′ is a shortest path.
But the topic is APSP which stands for "all pairs shortest paths" so I decided to just write SP instead and...
Is it written with a like this
therefore p′ is a SP
or with an like this (because in my head I would "read" the S)
therefore p′ is an SP
Whether you say a or an is determined by the pronunciation of the next word, and nothing else. If the next word begins with a consonant sound (not necessarily a consonant letter!), you say a, and if it begins with a vowel sound (not necessarily a vowel letter!), you say an.
So yes, you are correct: if you write or read "SP", you would say "an SP", because "ess" begins with a vowel sound.
These are actually called acronyms or initialisms. The few editing guides I checked (like this one from the American Psychological Association) say to use this guide:
The general rule for indefinite articles [before acronyms] is to use a before consonants and an before vowels. The trick here is to use your ears (how the acronym is pronounced), not your eyes (how it's spelled).
This means you have to "sound out" the word in your head to tell if it starts with a consonant sound or a vowel sound. Examples:
I checked this answer with an APA editor. (ayy pee ayy)
Today an FBI agent came to our office. (eff bee eye)
Today a CNN reporter asked me questions (cee enn enn)
Today an NBC reporter asked me questions (enn bee cee)
However, this depends on whether you commonly sound out the individual letters, or if the acronym is usually pronounced as a word. For example, a LAN (computer network) is usually pronounced as it's spelled, so you would say:
a LAN schematic
Similarly SAM, SIM, SCUBA, GIF, JPEG, ZIP, LASER, IMAX, and others.
Other examples:
- a FASB rule; an FOB airfield
- a LAN schematic; an LAPD memo
- a MOMA exhibit; an MRI test
- a NICU nurse; an NPO order
- a SAM base; an SAT exam
(Edit) To add further complication: As choster mentions below, not everyone pronounces all of these kind of abbreviations the same way. For example, with SQL, some people say "ess cue ell" and others say "sequel".
In the first case you would say, "an SQL query" and the second, "a SQL query"
I've left a comment already, and the OP has already selected the accepted answer, but I feel compelled to leave a full answer of my own because it feels like there are a number of loose ends.
First, it's well established that the use of a vs. an is determined by the sound that comes next, not necessarily the written letter. The Chicago Manual of Style (16th edition) puts it like this:
"A comes before words with a consonant sound...no matter how the word is spelled {a eulogy}"
But the OP seems to understand this already, based on the wording of his text. The title of this question has to do specifically with abbreviations. Here things get tricky. You should still chose the article adjective based on the sound it precedes. But when an abbreviation can be pronounced more than one way, and the pronunciation determines the article, how do you pick the correct article?
Some abbreviations are almost always pronounced as the full word or phrase that they represent:
Some abbreviations (intitialisms) tend to be pronounced letter by letter, while others (acronyms) tend to be prounounced as single words:
That leaves the 3rd class of abbreviations: Their pronunciation hasn't settled into a standard form yet. I think this is the part of the OP's question that the other responses haven't addressed and that feels like a loose end.
So in print: For abbreviations without a traditional, well-understood pronunciation, how do you choose the correct article adjective? How do you know if an abbreviation is meant to be read out loud as:
The use of all caps is no help. For example, if read out loud, don't you pronounce TBSP as "Tablespoon" and BLVD as "Boulevard"? I've seen Stack Exchanged abbreviated as "S.E.," but don't you still read that aloud as Stack Exchange?
I would put the OP's "SP" in this category since it's a non-standard abbreviation that the OP came up with him/herself. I can think of three options to pick the right article:
"Before an abbreviation, a numeral, or a symbol, the use of a or an depends on (or conversely determines) how the term is pronounced." [emphasis mine]
In other words, you can choose whichever article adjective you prefer, and that should guide the reader how you intend the abbreviation to be pronounced.
The general rule is that when the initial letter of a word has a consonant sound, article "a" takes precedence and when it's a vowel sound, article "an" is used. This however depends on the pronunciation of certain words inform of initials, acronyms or abbreviations.
