Abstract
We consider the problem of estimating the length of a shortest path in a DAG whose edge lengths are known only approximately but can be determined exactly at a cost. Initially, each edge e is known only to lie within an interval [l e , h e ]; the estimation algorithm can pay c e to find the exact length of e. In particular, we study the problem of finding the cheapest set of edges such that, if exactly these edges are queried, the length of the shortest path will be known, within an additive k > 0 that is given as an input parameter. We study both the general problem and several special cases, and obtain both easiness and hardness approximation results.
Department of Computer Science, Stanford University, Stanford, CA 94305. Research supported by NSF Grant IIS-0118173, an Okawa Foundation Research Grant, and Veritas.
Department of Computer Science, Stanford University, Stanford, CA 94305. Research supported by an NSF Graduate Fellowship, an ARCS Fellowship, and NSF Grants IIS-0118173, IIS-9811904, and EIA-0137761.
Department of Computer Science, Stanford University, Stanford, CA 94305. Research supported by an NSF Graduate Research Fellowship, and by NSF Grants IIS-9817799, IIS-9811947, and IIS-0118173.
Cisco Systems.
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Feder, T., Motwani, R., O’Callaghan, L., Olston, C., Panigrahy, R. (2003). Computing Shortest Paths with Uncertainty. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_33
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DOI: https://doi.org/10.1007/3-540-36494-3_33
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