264 research outputs found
Solving the Generalized Steiner Problem in edge-survivable networks
The Generalized Steiner Problem with Edge-Connectivity constraints (GSP-EC) consists of computing the minimal cost subnetwork of a given feasible network where some pairs of nodes must satisfy edge-connectivity requirements. It can be applied in the design of communications networks where connection lines can fail and is known to be an NP-Complete problem. In this paper we introduce an algorithm based on GRASP (Greedy Randomized Adaptive Search Procedure), a combinatorial optimization metaheuristic that has proven to be very effective for such problems. Promising results are obtained when testing the algorithm over a set of heterogeneous network topologies and connectivity requirements; in all cases with known optimal cost, optimal or near-optimal solutions are found
Non-Uniform Robust Network Design in Planar Graphs
Robust optimization is concerned with constructing solutions that remain
feasible also when a limited number of resources is removed from the solution.
Most studies of robust combinatorial optimization to date made the assumption
that every resource is equally vulnerable, and that the set of scenarios is
implicitly given by a single budget constraint. This paper studies a robustness
model of a different kind. We focus on \textbf{bulk-robustness}, a model
recently introduced~\cite{bulk} for addressing the need to model non-uniform
failure patterns in systems.
We significantly extend the techniques used in~\cite{bulk} to design
approximation algorithm for bulk-robust network design problems in planar
graphs. Our techniques use an augmentation framework, combined with linear
programming (LP) rounding that depends on a planar embedding of the input
graph. A connection to cut covering problems and the dominating set problem in
circle graphs is established. Our methods use few of the specifics of
bulk-robust optimization, hence it is conceivable that they can be adapted to
solve other robust network design problems.Comment: 17 pages, 2 figure
Improved Algorithm for Degree Bounded Survivable Network Design Problem
We consider the Degree-Bounded Survivable Network Design Problem: the
objective is to find a minimum cost subgraph satisfying the given connectivity
requirements as well as the degree bounds on the vertices. If we denote the
upper bound on the degree of a vertex v by b(v), then we present an algorithm
that finds a solution whose cost is at most twice the cost of the optimal
solution while the degree of a degree constrained vertex v is at most 2b(v) +
2. This improves upon the results of Lau and Singh and that of Lau, Naor,
Salavatipour and Singh
Survivable Networks, Linear Programming Relaxations and the Parsimonious Property
We consider the survivable network design problem - the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the k-connected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worstcase analyses of two heuristics for the survivable network design problem
Covering problems in edge- and node-weighted graphs
This paper discusses the graph covering problem in which a set of edges in an
edge- and node-weighted graph is chosen to satisfy some covering constraints
while minimizing the sum of the weights. In this problem, because of the large
integrality gap of a natural linear programming (LP) relaxation, LP rounding
algorithms based on the relaxation yield poor performance. Here we propose a
stronger LP relaxation for the graph covering problem. The proposed relaxation
is applied to designing primal-dual algorithms for two fundamental graph
covering problems: the prize-collecting edge dominating set problem and the
multicut problem in trees. Our algorithms are an exact polynomial-time
algorithm for the former problem, and a 2-approximation algorithm for the
latter problem, respectively. These results match the currently known best
results for purely edge-weighted graphs.Comment: To appear in SWAT 201
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