Point Lookout: a free weekly publication of Chaco Canyon Consulting
Volume 10, Issue 42;   October 20, 2010: Forward Backtracking

Forward Backtracking

by

The nastiest part about solving complex problems isn't their complexity. It's the feeling of being overwhelmed when we realize we haven't a clue about how to get from where we are to where we need to be. Here's one way to get a clue.
Part of one of the tunnel boring machines used to build the tunnel under the English Channel

Part of one of the tunnel boring machines used to build the tunnel under the English Channel. The Chunnel, like many long tunnels, was constructed by boring from both ends. Actually, boring machines worked in two directions from access points in both France and the U.K. The French and British efforts met under the channel on October 30, 1990, just under three years after boring operations began.

Tunnel boring provides an intriguing metaphor for forward backtracking. One advantage of forward backtracking not mentioned in this article is that, like tunnel boring, we can apply effort at both ends simultaneously. While one team tries to solve the problem in the forward sense, another can work out solutions using backtracking. The two teams can then assemble periodically and share insights, accelerating the work at both ends. In the case of the Chunnel, boring operations on either side of the Channel proceeded in both directions from access points near shore. By analogy, we can see that sometimes it's useful to break a problem into segments, and solve it in both directions from each of the segment boundaries. Photo courtesy BBC.

Nearly every morning, if I'm in town, I do a two-and-a-half mile loop around Fresh Pond, in Cambridge, Massachusetts. I usually go at about dawn. It's peaceful, quiet, and still, with plenty of opportunities to observe the kind of wildlife you find in urban parks. Today it was rabbits, cormorants, a hawk, and of course, some dogs walking their people.

Sometimes I vary my routine. For example, I might combine the trip with a trip to the automatic teller machine at a nearby bank. When I do that, I have to figure out where to leave the pond path for the climb through the woods over the multiple branching paths that lead up to the street to go to the bank. Until recently, I always emerged from the woods too far to the northeast. I never could find the right path through the woods.

Last week I had an idea. I reversed direction, going to the bank first, then down to the pond and around the pond path. That way, I could be sure to be on the right path through the woods. Well, it worked, of course. Duh.

Point is, the next time I want to get from the pond path to the automatic teller machine at the bank, I know how to do it, because I've been over the path before.

I call this forward backtracking. By beginning at the end, and ending at the beginning, you can figure out how to begin at the beginning and end at the end.

Strangely enough, forward backtracking applies far beyond getting from Fresh Pond to my bank. It's useful for solving the most complex problems, like adjusting a 20-month project schedule to meet an imposed deadline. A problem like that can be daunting, because it involves scheduling, resources, budgets, and — inevitably — politics.

The By beginning at the end,
and ending at the beginning,
you can figure out how
to begin at the beginning
and end at the end
usual approach to such problems starts with creating lists of possible solution ideas. Then we apply them, one-by-one, or in combination, until we find something that works. If nothing works, we look for more ideas.

Forward backtracking provides some alternative approaches.

When looking for new ideas, we can apply forward backtracking by asking, "If we did have the solution, what would have been the last step that got us there?"

To discover people we might have forgotten to consult, we can ask, "If we did have a truly ingenious solution, who would have been most likely to have helped find it?"

Imaginary testing, too, can reveal attributes that help solutions: "If we had a candidate solution in hand, how would we know that it worked?"

Forward backtracking can help even beyond problem solving. For a new perspective on complex documents, try reviewing them back-to-front. And you need not worry — it won't spoil the ending. Go to top Top  Next issue: Sixteen Overload Haiku  Next Issue

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In this Part II of our look at solving hard problems, we continue developing properties of the solution, and look at how we get from the beginning to the end. Available here and by RSS on July 5.

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