9,791 research outputs found
On space efficiency of algorithms working on structural decompositions of graphs
Dynamic programming on path and tree decompositions of graphs is a technique
that is ubiquitous in the field of parameterized and exponential-time
algorithms. However, one of its drawbacks is that the space usage is
exponential in the decomposition's width. Following the work of Allender et al.
[Theory of Computing, '14], we investigate whether this space complexity
explosion is unavoidable. Using the idea of reparameterization of Cai and
Juedes [J. Comput. Syst. Sci., '03], we prove that the question is closely
related to a conjecture that the Longest Common Subsequence problem
parameterized by the number of input strings does not admit an algorithm that
simultaneously uses XP time and FPT space. Moreover, we complete the complexity
landscape sketched for pathwidth and treewidth by Allender et al. by
considering the parameter tree-depth. We prove that computations on tree-depth
decompositions correspond to a model of non-deterministic machines that work in
polynomial time and logarithmic space, with access to an auxiliary stack of
maximum height equal to the decomposition's depth. Together with the results of
Allender et al., this describes a hierarchy of complexity classes for
polynomial-time non-deterministic machines with different restrictions on the
access to working space, which mirrors the classic relations between treewidth,
pathwidth, and tree-depth.Comment: An extended abstract appeared in the proceedings of STACS'16. The new
version is augmented with a space-efficient algorithm for Dominating Set
using the Chinese remainder theore
Corporate payments networks and credit risk rating
Aggregate and systemic risk in complex systems are emergent phenomena
depending on two properties: the idiosyncratic risks of the elements and the
topology of the network of interactions among them. While a significant
attention has been given to aggregate risk assessment and risk propagation once
the above two properties are given, less is known about how the risk is
distributed in the network and its relations with the topology. We study this
problem by investigating a large proprietary dataset of payments among 2.4M
Italian firms, whose credit risk rating is known. We document significant
correlations between local topological properties of a node (firm) and its
risk. Moreover we show the existence of an homophily of risk, i.e. the tendency
of firms with similar risk profile to be statistically more connected among
themselves. This effect is observed when considering both pairs of firms and
communities or hierarchies identified in the network. We leverage this
knowledge to show the predictability of the missing rating of a firm using only
the network properties of the associated node
Learning Hierarchical Classifiers with Class Taxonomies
As more and more data with class taxonomies emerge in diverse fields, such as pattern recognition, text classification and gene function prediction, we need to extend traditional machine learning methods to solve classification problem in such data sets, which presents more challenges over common pattern classification problems. In this paper, we define structured label classification problem and investigate two learning approaches that can learn classifier in such data sets. We also develop distance metrics with label mapping strategy to evaluate the results. We present experimental results that demonstrate the promise of the proposed approaches
Methods for many-objective optimization: an analysis
Decomposition-based methods are often cited as the
solution to problems related with many-objective optimization. Decomposition-based methods employ a scalarizing function to reduce a many-objective problem into a set of single objective problems, which upon solution yields a good approximation of the set of optimal solutions. This set is commonly referred to as
Pareto front. In this work we explore the implications of using decomposition-based methods over Pareto-based methods from a probabilistic point of view. Namely, we investigate whether there is an advantage of using a decomposition-based method, for example using the Chebyshev scalarizing function, over Paretobased methods
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