Iterative packing for demand matching and sparse packing.
Conference
·
OSTI ID:1032921
The main result we will present is a 2k-approximation algorithm for the following 'k-hypergraph demand matching' problem: given a set system with sets of size <=k, where sets have profits & demands and vertices have capacities, find a max-profit subsystem whose demands do not exceed the capacities. The main tool is an iterative way to explicitly build a decomposition of the fractional optimum as 2k times a convex combination of integral solutions. If time permits we'll also show how the approach can be extended to a 3-approximation for 2-column sparse packing. The second result is tight w.r.t the integrality gap, and the first is near-tight as a gap lower bound of 2(k-1+1/k) is known.
- Research Organization:
- Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1032921
- Report Number(s):
- SAND2010-8137C; TRN: US201202%%474
- Resource Relation:
- Conference: Proposed for presentation at the Integer Programming and Combinatorial Optimization 2011 held June 15-17, 2011 in Yorktown Heights, NY.
- Country of Publication:
- United States
- Language:
- English
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