What approach would you take to reduce or eliminate these gang problems?
To get a better answer, please ask a more specific question. It is hard to know what "these gang problems" are. Also, if there are specific approaches we are to choose from, please provide those as well.
In general, gang problems are best addressed by a mixture of stronger law enforcement and what might be seen as social work. It is necessary to prove that gang activity will not be tolerated. This can be done through things like increased patrols of problem areas and the creation of a strong neighborhood watch organization. However, it is also necessary to work to reduce the conditions that lead youths to gang membership. It is important to provide activities like sports teams that can give young people a sense of belonging and pride. Youths who cannot find other ways to get these feelings tend to gravitate towards gangs in order to get them.
Thus, gang problems in general need to be attacked in a variety of ways.
The gang problem needs to be addressed by some creative, innovative, powerful thinkers, possibly a think tank, looking at social, economic, anthropological, legal, psychological,etc. factors together, to break the chain of influences that bring about the gang mentality and environment. It is not a problem that will solve itself, and it is very costly to our society. The money spent to think it out would be saved in prison costs. This should be an entire industry, maybe even a government bureau. Start by listing those features that all gangs have in common. Then assign responsibility to the social economic forces that feed them -- education shortcomings, racial identification, gun manufacturing, poor parenting (often because both parents work), single mothers, deadbeat fathers, corrupt or inefficient social support systems, hormones, media, etc. etc.