## Tuesday, September 04, 2007

### Preventing Wrong Numbers

Our phone number begins 244. A local business that rents out apartments begins 224. We get a lot of phone calls from people looking for apartments.

What might a phone company could do to prevent such problems? One possibility is to divide customers into two categories. Category A includes all customers, mostly commercial, who get a lot of phone calls from strangers. Category B includes all customers, mostly residential, who are likely to be bothered by wrong numbers. Assign numbers to the two groups in a way that makes it unlikely for an error in dialing a category A number to convert it into a category B number.

An alternative, starting with existing numbers, would be to calculate for each number its risk of being dialed by mistake. The calculation has three stages:

1. Research on what sort of errors people make in dialing--transposing, dialing an adjacent digit, and the like--and how likely they are.

2. For each phone number X, sum over all other numbers Yi the probability of misdialing X while trying to dial Yi times the number of calls per day that Yi currently receives.

3. Make a list of X's for which the sum is low--numbers unlikely to be misdialed--and offer them to customers at a premium price.

Anonymous said...

Presumably the "right thing" is to keep a tally of which phone numbers are dialed most often and attempt not to assign other numbers that have a close hamming distance from said numbers if possible.

However, they aren't going to do it -- this is the Teleban we're talking about.

As an aside, my business number was once one digit off of a popular restaurant. Sometimes in frustration I wondered if I should start accepting the reservations people so desperately wanted...

Lippard said...

How about replace phone numbers with some other kind of universal identifier? Isn't using phone numbers to call people something like using IP addresses to visit websites?

Arthur B. said...

In the future it's probable that phone number disappear under a layer of user chosen ids and online contact lists so the problem will be irrelevant.

Computing the error-distance between two phone numbers is quite easy, but selecting N phone numbers that maximize the minimal error distance is related to the independent set problem in a graph and NP-hard.

Anonymous said...

Growing up, my parents' phone number was slightly off from a grain elevator in the next town over. Sometimes when my dad was feeling ornery, he'd just take the call and quote them a ridiculously good asking price in an effort to teach farmers to pay more attention when dialing...

Anonymous said...

My personal solution is a combination of caller ID and voicemail. When my phone rings, I routinely ignore it unless I can tell who the caller is. People I want to talk to will leave a message identifying themselves so I can call them back (or I can pick up the phone before they hang up).

Repeat offenders who make numerous wrong-number calls to my cell phone get an entry and a nickname in my cell phone's phone book. Thus, when my phone vibrates, the caller is identified appropriately. I can see that it's just another call from "Wrong Number" or "For Bob" or "Dumb Ass" or "Muttonfingers" (apparently unable to dial accurately), and that I can ignore the call.

Although I still have to spare glance at my caller ID, this shifts most of the cost of misdialing (not getting an answer, having to wait for the phone to ring until voicemail picks up) back to the misdialer.

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