Name
Abstract | ||
|---|---|---|
We consider a special class of axial multi-dimensional assignment problems called multi-dimensional vector assignment (MVA) problems. An instance of the MVA problem is defined by m disjoint sets, each of which contains the same number n of p-dimensional vectors with nonnegative integral components, and a cost function defined on vectors. The cost of an m-tuple of vectors is defined as the cost of their component-wise maximum. The problem is now to partition the m sets of vectors into n m-tuples so that no two vectors from the same set are in the same m-tuple and so that the sum of the costs of the m-tuples is minimized. The main motivation comes from a yield optimization problem in semi-conductor manufacturing. We consider a particular class of polynomial-time heuristics for MVA, namely the sequential heuristics, and we study their approximation ratio. In particular, we show that when the cost function is monotone and subadditive, sequential heuristics have a finite approximation ratio for every fixed m. Moreover, we establish smaller approximation ratios when the cost function is submodular and, for a specific sequential heuristic, when the cost function is additive. We provide examples to illustrate the tightness of our analysis. Furthermore, we show that the MVA problem is APX-hard even for the case m=3 and for binary input vectors. Finally, we show that the problem can be solved in polynomial time in the special case of binary vectors with fixed dimension p. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.disopt.2014.08.005 | Discrete Optimization |
Keywords | Field | DocType |
Multi-dimensional assignment,Approximability,Worst-case analysis,Submodularity,Wafer-to-wafer integration | Discrete mathematics,Combinatorics,Mathematical optimization,Disjoint sets,Tuple,Submodular set function,Heuristics,Subadditivity,Time complexity,Optimization problem,Monotone polygon,Mathematics | Journal |
Volume | Issue | ISSN |
14 | C | 1572-5286 |
Citations | PageRank | References |
2 | 0.41 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Trivikram Dokka | 1 | 19 | 5.33 |
| Yves Crama | 2 | 547 | 63.94 |
| Frits C. R. Spieksma | 3 | 591 | 58.84 |