Suicide bombing is simply a tactic, along the same line as IEDs - and both have been used to varying degrees of success in the COE. However, as has been noted repeatedly, it is often referred to as a "strategic tactic", as it's impact can be distributed far beyond its immediate messy consequences by the broadcase media and virtual comms.

Personally, I feel it is pointless to look at a "root of the problem" for suicide bombing per se - we need to look to the root of the conflict and move from there. Each region where suicide bombing has been used to any significant degree has to be looked at in its own unique context - although there are certainly similarities.

We're dealing with the issue in Iraq (unprecedented numbers) and Afghanistan, then we have the LTTE as mentioned, the phenomenon of the Chechen "Black Widows" as well as female suicide bombers used by the Marxist PKK, and, of course, the spectrum of Palestinian suicide bombings. There are other examples, but my point is that to treat any or all of these situations in an identical manner is a mistake.
I'd say Hizbullah beat the LTTE to the punch, but the LTTE really molded effective suicide terrorism in the 1980s. How many suicide bombers has Hizbullah used compared to the LTTE? Also, the LTTE I'd argue has been far more effective.
Hezballah moved on from suicide bombings to refining their use of IEDs in their campaign against the IDF and SLA in South Lebanon (as well as more conventional military raid/ambush tactics), whereas the LTTE has continued to use suicide bombers across the spectrum.

FYI, aside from buying the book, here's Pape's article from the Aug 03 issue of American Political Science Review: The Strategic Logic of Suicide Terrorism
...Perhaps most important, the close association between foreign military occupations and the growth of suicide terrorist movements in the occupied regions should give pause to those who favor solutions that involve conquering countries in order to transform their political systems....
In sum, at the tactial level, we've developed an entire spectrum of countermeasures, identified indicators and continue to train and raise awareness of our soldiers and LE professionals. However, threat TTPs continue to evolve in the face of our countermeasures - there will never come a point when we are completely protected from suicide bombers or IEDs. When it comes down to it, the ultimate solution is what the community here at SWC has long been pushing - improved implementation of effective COIN. Make your list of buzz-words regarding interagency cooperation and building governance capabilities - as Troufion stated in his post at the head of this thread, addressing root causes means more than killing bad guys.