26,611 research outputs found
On robust network coding subgraph construction under uncertainty
We consider the problem of network coding subgraph
construction in networks where there is uncertainty about
link loss rates. For a given set of scenarios specified by an uncertainty
set of link loss rates, we provide a robust optimization-based
formulation to construct a single subgraph that would work
relatively well across all scenarios. We show that this problem
is coNP-hard in general for both objectives: minimizing cost
of subgraph construction and maximizing throughput given a
cost constraint. To solve the problem tractably, we approximate
the problem by introducing path constraints, which results
in polynomial time-solvable solution in terms of the problem
size. The simulation results show that the robust optimization
solution is better and more stable than the deterministic solution
in terms of worst-case performance. From these results, we
compare the tractability of robust network design problems with
different uncertain network components and different problem
formulations
On Generalizations of Network Design Problems with Degree Bounds
Iterative rounding and relaxation have arguably become the method of choice
in dealing with unconstrained and constrained network design problems. In this
paper we extend the scope of the iterative relaxation method in two directions:
(1) by handling more complex degree constraints in the minimum spanning tree
problem (namely, laminar crossing spanning tree), and (2) by incorporating
`degree bounds' in other combinatorial optimization problems such as matroid
intersection and lattice polyhedra. We give new or improved approximation
algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure
Robust Assignments via Ear Decompositions and Randomized Rounding
Many real-life planning problems require making a priori decisions before all
parameters of the problem have been revealed. An important special case of such
problem arises in scheduling problems, where a set of tasks needs to be
assigned to the available set of machines or personnel (resources), in a way
that all tasks have assigned resources, and no two tasks share the same
resource. In its nominal form, the resulting computational problem becomes the
\emph{assignment problem} on general bipartite graphs.
This paper deals with a robust variant of the assignment problem modeling
situations where certain edges in the corresponding graph are \emph{vulnerable}
and may become unavailable after a solution has been chosen. The goal is to
choose a minimum-cost collection of edges such that if any vulnerable edge
becomes unavailable, the remaining part of the solution contains an assignment
of all tasks.
We present approximation results and hardness proofs for this type of
problems, and establish several connections to well-known concepts from
matching theory, robust optimization and LP-based techniques.Comment: Full version of ICALP 2016 pape
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