277 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Utilitarian Welfare Optimization in the Generalized Vertex Coloring Games: An Implication to Venue Selection in Events Planning
We consider a general class of multi-agent games in networks, namely the
generalized vertex coloring games (G-VCGs), inspired by real-life applications
of the venue selection problem in events planning. Certain utility responding
to the contemporary coloring assignment will be received by each agent under
some particular mechanism, who, striving to maximize his own utility, is
restricted to local information thus self-organizing when choosing another
color. Our focus is on maximizing some utilitarian-looking welfare objective
function concerning the cumulative utilities across the network in a
decentralized fashion. Firstly, we investigate on a special class of the
G-VCGs, namely Identical Preference VCGs (IP-VCGs) which recovers the
rudimentary work by \cite{chaudhuri2008network}. We reveal its convergence even
under a completely greedy policy and completely synchronous settings, with a
stochastic bound on the converging rate provided. Secondly, regarding the
general G-VCGs, a greediness-preserved Metropolis-Hasting based policy is
proposed for each agent to initiate with the limited information and its
optimality under asynchronous settings is proved using theories from the
regular perturbed Markov processes. The policy was also empirically witnessed
to be robust under independently synchronous settings. Thirdly, in the spirit
of ``robust coloring'', we include an expected loss term in our objective
function to balance between the utilities and robustness. An optimal coloring
for this robust welfare optimization would be derived through a second-stage
MH-policy driven algorithm. Simulation experiments are given to showcase the
efficiency of our proposed strategy.Comment: 35 Page
Sum-of-squares representations for copositive matrices and independent sets in graphs
A polynomial optimization problem asks for minimizing a polynomial function (cost) given a set of constraints (rules) represented by polynomial inequalities and equations. Many hard problems in combinatorial optimization and applications in operations research can be naturally encoded as polynomial optimization problems. A common approach for addressing such computationally hard problems is by considering variations of the original problem that give an approximate solution, and that can be solved efficiently. One such approach for attacking hard combinatorial problems and, more generally, polynomial optimization problems, is given by the so-called sum-of-squares approximations. This thesis focuses on studying whether these approximations find the optimal solution of the original problem.We investigate this question in two main settings: 1) Copositive programs and 2) parameters dealing with independent sets in graphs. Among our main new results, we characterize the matrix sizes for which sum-of-squares approximations are able to capture all copositive matrices. In addition, we show finite convergence of the sums-of-squares approximations for maximum independent sets in graphs based on their continuous copositive reformulations. We also study sum-of-squares approximations for parameters asking for maximum balanced independent sets in bipartite graphs. In particular, we find connections with the Lovász theta number and we design eigenvalue bounds for several related parameters when the graphs satisfy some symmetry properties.<br/
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization
Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes
2023-2024 academic bulletin & course catalog
University of South Carolina Aiken publishes a catalog with information about the university, student life, undergraduate and graduate academic programs, and faculty and staff listings
Heckerthoughts
This manuscript is technical memoir about my work at Stanford and Microsoft
Research. Included are fundamental concepts central to machine learning and
artificial intelligence, applications of these concepts, and stories behind
their creation
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Fundamentals
Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters
-matchings Parameterized by Treewidth
A \emph{matching} is a subset of edges in a graph that do not share an
endpoint. A matching is a \emph{-matching} if the subgraph of
induced by the endpoints of the edges of satisfies property
. For example, if the property is that of being a
matching, being acyclic, or being disconnected, then we obtain an \emph{induced
matching}, an \emph{acyclic matching}, and a \emph{disconnected matching},
respectively. In this paper, we analyze the problems of the computation of
these matchings from the viewpoint of Parameterized Complexity with respect to
the parameter \emph{treewidth}.Comment: To Appear in the proceedings of WG 202
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