Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Improved Approximation Algorithms for Unsplittable Flow Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximating the single source unsplittable min-cost flow problem
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
How good can IP routing be?
Internet Routing and Related Topology Issues
SIAM Journal on Discrete Mathematics
Increasing Internet Capacity Using Local Search
Computational Optimization and Applications
An Integer Programming Algorithm for Routing Optimization in IP Networks
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
How bad is single-path routing
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Cost of not splitting in routing: characterization and estimation
IEEE/ACM Transactions on Networking (TON)
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We are given an undirected simple graph G = (V,E) with edge capacities $c_{e} \epsilon \mathcal{Z}+$, e ∈ E, and a set K⊆V2 of commodities with demand values d(s,t)εℤ, (s, t) ∈ K. An unsplittable shortest path routing (USPR) of the commodities K is a set of flow paths Φ(s,t), (s, t) ∈ K, such that each Φ(s,t) is the unique shortest (s, t)-path for commodity (s, t) with respect to a common edge length function $\lambda = (\lambda_e) \epsilon \mathbb{Z}^{E}_{+}$. The minimum congestion unsplittable shortest path routing problem (Min-Con-USPR) is to find an USPR that minimizes the maximum congestion (i.e., the flow to capacity ratio) over all edges. We show that it is $\mathcal{NP}$-hard to approximate Min-Con-USPR within a factor of $\mathcal{O}(|V|^1-\epsilon)$ for any ε 0. We also present a simple approximation algorithm that achieves an approximation guarantee of $\mathcal{O}(|E|)$ in the general case and of 2 in the special case where the underlying graph G is a cycle. Finally, we construct examples where the minimum congestion that can be obtained with an USPR is a factor of Ω(|V|2) larger than the congestion of an optimal unsplittable flow routing or an optimal shortest multi-path routing, and a factor of Ω(|V|) larger than the congestion of an optimal unsplittable source-invariant routing. This indicates that unsplittable shortest path routing problems are indeed harder than their corresponding unsplittable flow, shortest multi-path, and unsplittable source-invariant routing problems. The Min-Con-USPR problem is of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Mathematical Subject Classification (2000): 68Q25, 90C60, 90C27, 05C38, 90B18.