432 research outputs found
Approximability of Robust Network Design: The Directed Case
We consider robust network design problems where an uncertain traffic vector belonging to a polytope has to be dynamically routed to minimize either the network congestion or some linear reservation cost. We focus on the variant in which the underlying graph is directed. We prove that an O(?k) = O(n)-approximation can be obtained by solving the problem under static routing, where k is the number of commodities and n is the number of nodes. This improves previous results of Hajiaghayi et al. [SODA\u272005] and matches the ?(n) lower bound of Ene et al. [STOC\u272016] and the ?(?k) lower bound of Azar et al. [STOC\u272003]. Finally, we introduce a slightly more general problem version where some flow restrictions can be added. We show that it cannot be approximated within a ratio of k^{c/(log log k)} (resp. n^{c/(log log n)}) for some constant c. Making use of a weaker complexity assumption, we prove that there is no approximation within a factor of 2^{log^{1- ?} k} (resp. 2^{log^{1- ?} n}) for any ? > 0
Survivability and performance optimization in communication networks using network coding
The benefits of network coding are investigated in two types of communication networks: optical backbone networks and wireless networks. In backbone networks, network coding is used to improve survivability of the network against failures. In particular, network coding-based protection schemes are presented for unicast and multicast traffic models. In the unicast case, network coding was previously shown to offer near-instantaneous failure recovery at the bandwidth cost of shared backup path protection. Here, cost-effective polynomial-time heuristic algorithms are proposed for online provisioning and protection of unicast traffic. In the multicast case, network coding is used to extend the traditional live backup (1+1) unicast protection to multicast protection; hence called multicast 1+1 protection. It provides instantaneous recovery for single failures in any bi-connected network with the minimum bandwidth cost. Optimal formulation and efficient heuristic algorithms are proposed and experimentally evaluated. In wireless networks, performance benefits of network coding in multicast transmission are studied. Joint scheduling and performance optimization formulations are presented for rate, energy, and delay under routing and network coding assumptions. The scheduling component of the problem is simplified by timesharing over randomly-selected sets of non-interfering wireless links. Selecting only a linear number of such sets is shown to be rate and energy effective. While routing performs very close to network coding in terms of rate, the solution convergence time is around 1000-fold compared to network coding. It is shown that energy benefit of network coding increases as the multicast rate demand is increased. Investigation of energy-rate and delay-rate relationships shows both parameters increase non-linearly as the multicast rate is increased
Shortest Path versus Multi-Hub Routing in Networks with Uncertain Demand
We study a class of robust network design problems motivated by the need to
scale core networks to meet increasingly dynamic capacity demands. Past work
has focused on designing the network to support all hose matrices (all matrices
not exceeding marginal bounds at the nodes). This model may be too conservative
if additional information on traffic patterns is available. Another extreme is
the fixed demand model, where one designs the network to support peak
point-to-point demands. We introduce a capped hose model to explore a broader
range of traffic matrices which includes the above two as special cases. It is
known that optimal designs for the hose model are always determined by
single-hub routing, and for the fixed- demand model are based on shortest-path
routing. We shed light on the wider space of capped hose matrices in order to
see which traffic models are more shortest path-like as opposed to hub-like. To
address the space in between, we use hierarchical multi-hub routing templates,
a generalization of hub and tree routing. In particular, we show that by adding
peak capacities into the hose model, the single-hub tree-routing template is no
longer cost-effective. This initiates the study of a class of robust network
design (RND) problems restricted to these templates. Our empirical analysis is
based on a heuristic for this new hierarchical RND problem. We also propose
that it is possible to define a routing indicator that accounts for the
strengths of the marginals and peak demands and use this information to choose
the appropriate routing template. We benchmark our approach against other
well-known routing templates, using representative carrier networks and a
variety of different capped hose traffic demands, parameterized by the relative
importance of their marginals as opposed to their point-to-point peak demands
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Combinatorial Optimization
Combinatorial Optimization is a very active field that benefits from bringing together ideas from different areas, e.g., graph theory and combinatorics, matroids and submodularity, connectivity and network flows, approximation algorithms and mathematical programming, discrete and computational geometry, discrete and continuous problems, algebraic and geometric methods, and applications. We continued the long tradition of triannual Oberwolfach workshops, bringing together the best researchers from the above areas, discovering new connections, and establishing new and deepening existing international collaborations
Optimal Cell Clustering and Activation for Energy Saving in Load-Coupled Wireless Networks
Optimizing activation and deactivation of base station transmissions provides
an instrument for improving energy efficiency in cellular networks. In this
paper, we study optimal cell clustering and scheduling of activation duration
for each cluster, with the objective of minimizing the sum energy, subject to a
time constraint of delivering the users' traffic demand. The cells within a
cluster are simultaneously in transmission and napping modes, with cluster
activation and deactivation, respectively. Our optimization framework accounts
for the coupling relation among cells due to the mutual interference. Thus, the
users' achievable rates in a cell depend on the cluster composition. On the
theoretical side, we provide mathematical formulation and structural
characterization for the energy-efficient cell clustering and scheduling
optimization problem, and prove its NP hardness. On the algorithmic side, we
first show how column generation facilitates problem solving, and then present
our notion of local enumeration as a flexible and effective means for dealing
with the trade-off between optimality and the combinatorial nature of cluster
formation, as well as for the purpose of gauging the deviation from optimality.
Numerical results demonstrate that our solutions achieve more than 60% energy
saving over existing schemes, and that the solutions we obtain are within a few
percent of deviation from global optimum.Comment: Revision, IEEE Transactions on Wireless Communication
Robust network optimization under polyhedral demand uncertainty is NP-hard
AbstractMinimum cost network design/dimensioning problems where feasibility has to be ensured w.r.t. a given (possibly infinite) set of scenarios of requirements form an important subclass of robust LP problems with right-hand side uncertainty. Such problems arise in many practical contexts such as Telecommunications, logistic networks, power distribution networks, etc. Though some evidence of the computational difficulty of such problems can be found in the literature, no formal NP-hardness proof was available up to now. In the present paper, this pending complexity issue is settled for all robust network optimization problems featuring polyhedral demand uncertainty, both for the single-commodity and multicommodity case, even if the corresponding deterministic versions are polynomially solvable as regular (continuous) linear programs. A new family of polynomially solvable instances is also discussed
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