Infrastructure Leasing Problems

Consider the following Steiner Tree leasing problem. Given a graph G= (V,E) with root r, and a sequence of terminal sets D t i¾? Vfor each day ti¾? [T]. A feasible solution to the problem is a set of edges E t for each tconnecting D t to r. Instead of obtaining edges for a single day at a time, or for infinitely long (both of which give Steiner tree problems), we leaseedges for say, { a day, a week, a month, a year}. Naturally, leasing an edge for a longer period costs less per unit of time. What is a good leasing strategy? In this paper, we give a general approach to solving a wide class of such problems by showing a close connection between deterministic leasing problems and problems in multistage stochastic optimization. All our results are in the offline setting.

[1]  Yossi Azar,et al.  Buy-at-bulk network design , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[2]  R. Ravi,et al.  Boosted sampling: approximation algorithms for stochastic optimization , 2004, STOC '04.

[3]  Yossi Azar,et al.  On-line generalized Steiner problem , 1996, SODA '96.

[4]  Prakash Mirchandani,et al.  CAPACITATED NETWORK LOADING PROBLEM , 1991 .

[5]  Leen Stougie,et al.  The stochastic single resource service‐provision problem , 2003 .

[6]  Lisa Zhang,et al.  Wavelength Assignment in Optical Networks with Fixed Fiber Capacity , 2004, ICALP.

[7]  R. Ravi,et al.  What About Wednesday? Approximation Algorithms for Multistage Stochastic Optimization , 2005, APPROX-RANDOM.

[8]  S. K. Goyal,et al.  Recent trends in modeling of deteriorating inventory , 2001, Eur. J. Oper. Res..

[9]  Satish Rao,et al.  A tight bound on approximating arbitrary metrics by tree metrics , 2003, STOC '03.

[10]  Robert D. Carr,et al.  Strengthening integrality gaps for capacitated network design and covering problems , 2000, SODA '00.

[11]  Vijay V. Vazirani,et al.  Equitable cost allocations via primal-dual-type algorithms , 2002, STOC '02.

[12]  Prabhakar Raghavan,et al.  Randomized rounding: A technique for provably good algorithms and algorithmic proofs , 1985, Comb..

[13]  R. Ravi,et al.  Approximating the Single-Sink Link-Installation Problem in Network Design , 2001, SIAM J. Optim..

[14]  Stefano Leonardi,et al.  Cross-monotonic cost-sharing methods for connected facility location games , 2004, EC '04.

[15]  Adam Meyerson.  The parking permit problem , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[16]  Stavros G. Kolliopoulos,et al.  Tight approximation results for general covering integer programs , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[17]  Aravind Srinivasan,et al.  Approximation algorithms for stochastic and risk-averse optimization , 2007, SODA '07.

[18]  Aravind Srinivasan,et al.  Improved Approximation Guarantees for Packing and Covering Integer Programs , 1999, SIAM J. Comput..

[19]  Thomas L. Magnanti,et al.  Network Design and Transportation Planning: Models and Algorithms , 1984, Transp. Sci..

[20]  Mauro Dell'Amico,et al.  Annotated Bibliographies in Combinatorial Optimization , 1997 .

[21]  R. Ravi,et al.  Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems , 2004, Math. Program..

[22]  Moses Charikar,et al.  Sampling Bounds for Stochastic Optimization , 2005, APPROX-RANDOM.

[23]  Aravind Srinivasan,et al.  New approaches to covering and packing problems , 2001, SODA '01.

[24]  Aravind Srinivasan,et al.  Cost-Sharing Mechanisms for Network Design , 2007, Algorithmica.

[25]  Nicole Immorlica,et al.  On the costs and benefits of procrastination: approximation algorithms for stochastic combinatorial optimization problems , 2004, SODA '04.

[26]  Steven Nahmias,et al.  Perishable Inventory Theory: A Review , 1982, Oper. Res..

[27]  Thomas L. Magnanti,et al.  Modeling and Solving the Two-Facility Capacitated Network Loading Problem , 1995, Oper. Res..

[28]  Chaitanya Swamy,et al.  Network design for information networks , 2005, SODA '05.

[29]  Mohit Singh,et al.  On Two-Stage Stochastic Minimum Spanning Trees , 2005, IPCO.

[30]  Sudipto Guha,et al.  Hierarchical placement and network design problems , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[31]  R. Ravi,et al.  On the Integrality Gap of a Natural Formulation of the Single-Sink Buy-at-Bulk Network Design Problem , 2001, IPCO.

[32]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[33]  Martin Skutella,et al.  New Approaches for Virtual Private Network Design , 2005, ICALP.

[34]  Kunal Talwar,et al.  The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap , 2002, IPCO.

[35]  Chaitanya Swamy,et al.  Stochastic optimization is (almost) as easy as deterministic optimization , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[36]  Yair Bartal,et al.  Probabilistic approximation of metric spaces and its algorithmic applications , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[37]  Chaitanya Swamy,et al.  Sampling-based approximation algorithms for multi-stage stochastic optimization , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[38]  Tim Roughgarden,et al.  Simpler and better approximation algorithms for network design , 2003, STOC '03.