1,378 research outputs found
User-Base Station Association in HetSNets: Complexity and Efficient Algorithms
This work considers the problem of user association to small-cell base
stations (SBSs) in a heterogeneous and small-cell network (HetSNet). Two
optimization problems are investigated, which are maximizing the set of
associated users to the SBSs (the unweighted problem) and maximizing the set of
weighted associated users to the SBSs (the weighted problem), under
signal-to-interference-plus-noise ratio (SINR) constraints. Both problems are
formulated as linear integer programs. The weighted problem is known to be
NP-hard and, in this paper, the unweighted problem is proved to be NP-hard as
well. Therefore, this paper develops two heuristic polynomial-time algorithms
to solve both problems. The computational complexity of the proposed algorithms
is evaluated and is shown to be far more efficient than the complexity of the
optimal brute-force (BF) algorithm. Moreover, the paper benchmarks the
performance of the proposed algorithms against the BF algorithm, the
branch-and-bound (B\&B) algorithm and standard algorithms, through numerical
simulations. The results demonstrate the close-to-optimal performance of the
proposed algorithms. They also show that the weighted problem can be solved to
provide solutions that are fair between users or to balance the load among
SBSs
Multiscale approach for the network compression-friendly ordering
We present a fast multiscale approach for the network minimum logarithmic
arrangement problem. This type of arrangement plays an important role in a
network compression and fast node/link access operations. The algorithm is of
linear complexity and exhibits good scalability which makes it practical and
attractive for using on large-scale instances. Its effectiveness is
demonstrated on a large set of real-life networks. These networks with
corresponding best-known minimization results are suggested as an open
benchmark for a research community to evaluate new methods for this problem
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
A Logical Approach to Efficient Max-SAT solving
Weighted Max-SAT is the optimization version of SAT and many important
problems can be naturally encoded as such. Solving weighted Max-SAT is an
important problem from both a theoretical and a practical point of view. In
recent years, there has been considerable interest in finding efficient solving
techniques. Most of this work focus on the computation of good quality lower
bounds to be used within a branch and bound DPLL-like algorithm. Most often,
these lower bounds are described in a procedural way. Because of that, it is
difficult to realize the {\em logic} that is behind.
In this paper we introduce an original framework for Max-SAT that stresses
the parallelism with classical SAT. Then, we extend the two basic SAT solving
techniques: {\em search} and {\em inference}. We show that many algorithmic
{\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in
{\em logic} terms with our framework in a unified manner.
Besides, we introduce an original search algorithm that performs a restricted
amount of {\em weighted resolution} at each visited node. We empirically
compare our algorithm with a variety of solving alternatives on several
benchmarks. Our experiments, which constitute to the best of our knowledge the
most comprehensive Max-sat evaluation ever reported, show that our algorithm is
generally orders of magnitude faster than any competitor
Risk-Averse Matchings over Uncertain Graph Databases
A large number of applications such as querying sensor networks, and
analyzing protein-protein interaction (PPI) networks, rely on mining uncertain
graph and hypergraph databases. In this work we study the following problem:
given an uncertain, weighted (hyper)graph, how can we efficiently find a
(hyper)matching with high expected reward, and low risk?
This problem naturally arises in the context of several important
applications, such as online dating, kidney exchanges, and team formation. We
introduce a novel formulation for finding matchings with maximum expected
reward and bounded risk under a general model of uncertain weighted
(hyper)graphs that we introduce in this work. Our model generalizes
probabilistic models used in prior work, and captures both continuous and
discrete probability distributions, thus allowing to handle privacy related
applications that inject appropriately distributed noise to (hyper)edge
weights. Given that our optimization problem is NP-hard, we turn our attention
to designing efficient approximation algorithms. For the case of uncertain
weighted graphs, we provide a -approximation algorithm, and a
-approximation algorithm with near optimal run time. For the case
of uncertain weighted hypergraphs, we provide a
-approximation algorithm, where is the rank of the
hypergraph (i.e., any hyperedge includes at most nodes), that runs in
almost (modulo log factors) linear time.
We complement our theoretical results by testing our approximation algorithms
on a wide variety of synthetic experiments, where we observe in a controlled
setting interesting findings on the trade-off between reward, and risk. We also
provide an application of our formulation for providing recommendations of
teams that are likely to collaborate, and have high impact.Comment: 25 page
Low-rank semidefinite programming for the MAX2SAT problem
This paper proposes a new algorithm for solving MAX2SAT problems based on
combining search methods with semidefinite programming approaches. Semidefinite
programming techniques are well-known as a theoretical tool for approximating
maximum satisfiability problems, but their application has traditionally been
very limited by their speed and randomized nature. Our approach overcomes this
difficult by using a recent approach to low-rank semidefinite programming,
specialized to work in an incremental fashion suitable for use in an exact
search algorithm. The method can be used both within complete or incomplete
solver, and we demonstrate on a variety of problems from recent competitions.
Our experiments show that the approach is faster (sometimes by orders of
magnitude) than existing state-of-the-art complete and incomplete solvers,
representing a substantial advance in search methods specialized for MAX2SAT
problems.Comment: Accepted at AAAI'19. The code can be found at
https://github.com/locuslab/mixsa
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