160,750 research outputs found
Dynamic Algorithms for Packing-Covering LPs via Multiplicative Weight Updates
In the dynamic linear program (LP) problem, we are given an LP undergoing
updates and we need to maintain an approximately optimal solution. Recently,
significant attention (e.g., [Gupta et al. STOC'17; Arar et al. ICALP'18, Wajc
STOC'20]) has been devoted to the study of special cases of dynamic packing and
covering LPs, such as the dynamic fractional matching and set cover problems.
But until now, there is no non-trivial dynamic algorithm for general packing
and covering LPs.
In this paper, we settle the complexity of dynamic packing and covering LPs,
up to a polylogarithmic factor in update time. More precisely, in the partially
dynamic setting (where updates can either only relax or only restrict the
feasible region), we give near-optimal deterministic -approximation
algorithms with polylogarithmic amortized update time. Then, we show that both
partially dynamic updates and amortized update time are necessary; without any
of these conditions, the trivial algorithm that recomputes the solution from
scratch after every update is essentially the best possible, assuming SETH.
To obtain our results, we initiate a systematic study of the multiplicative
weights update (MWU) method in the dynamic setting. As by-products of our
techniques, we also obtain the first online -competitive
algorithms for both covering and packing LPs with polylogarithmic recourse, and
the first streaming algorithms for covering and packing LPs with linear space
and polylogarithmic passes
Better Streaming Algorithms for the Maximum Coverage Problem
We study the classic NP-Hard problem of finding the maximum k-set coverage in the data stream model: given a set system of m sets that are subsets of a universe {1,...,n}, find the k sets that cover the most number of distinct elements. The problem can be approximated up to a factor 1-1/e in polynomial time. In the streaming-set model, the sets and their elements are revealed online. The main goal of our work is to design algorithms, with approximation guarantees as close as possible to 1-1/e, that use sublinear space o(mn). Our main results are: 1) Two (1-1/e-epsilon) approximation algorithms: One uses O(1/epsilon) passes and O(k/epsilon^2 polylog(m,n)) space whereas the other uses only a single pass but O(m/epsilon^2 polylog(m,n)) space. 2) We show that any approximation factor better than (1-(1-1/k)^k) in constant passes require space that is linear in m for constant k even if the algorithm is allowed unbounded processing time. We also demonstrate a single-pass, (1-epsilon) approximation algorithm using O(m/epsilon^2 min(k,1/epsilon) polylog(m,n)) space.
We also study the maximum k-vertex coverage problem in the dynamic graph stream model. In this model, the stream consists of edge insertions and deletions of a graph on N vertices. The goal is to find k vertices that cover the most number of distinct edges. We show that any constant approximation in constant passes requires space that is linear in N for constant k whereas O(N/epsilon^2 polylog(m,n)) space is sufficient for a (1-epsilon) approximation and arbitrary k in a single pass. For regular graphs, we show that O(k/epsilon^3 polylog(m,n)) space is sufficient for a (1-epsilon) approximation in a single pass. We generalize this to a K-epsilon approximation when the ratio between the minimum and maximum degree is bounded below by K
Facility Location in Evolving Metrics
Understanding the dynamics of evolving social or infrastructure networks is a
challenge in applied areas such as epidemiology, viral marketing, or urban
planning. During the past decade, data has been collected on such networks but
has yet to be fully analyzed. We propose to use information on the dynamics of
the data to find stable partitions of the network into groups. For that
purpose, we introduce a time-dependent, dynamic version of the facility
location problem, that includes a switching cost when a client's assignment
changes from one facility to another. This might provide a better
representation of an evolving network, emphasizing the abrupt change of
relationships between subjects rather than the continuous evolution of the
underlying network. We show that in realistic examples this model yields indeed
better fitting solutions than optimizing every snapshot independently. We
present an -approximation algorithm and a matching hardness result,
where is the number of clients and the number of time steps. We also
give an other algorithms with approximation ratio for the variant
where one pays at each time step (leasing) for each open facility
Fast flux botnet detection framework using adaptive dynamic evolving spiking neural network algorithm
A botnet, a set of compromised machines controlled
distantly by an attacker, is the basis of numerous security threats around the world. Command and Control servers are the backbones of botnet communications, where the bots and botmasters send report and attack orders to each other. Botnets are also categorized according to their C&C protocols.
A Domain Name System method known as Fast-Flux Service Network (FFSN) – a special type of botnet – has been engaged by bot herders to cover malicious botnet
activities and increase the lifetime of malicious servers by quickly changing the IP addresses of the domain name over time. Although several methods have been suggested for detecting FFSNs, they have low detection accuracy especially with zero-day domain. In this
research, we propose a new system called Fast Flux Killer System (FFKS) that has the ability to detect FF-Domains in online mode with an implementation constructed on Adaptive Dynamic evolving Spiking Neural Network (ADeSNN). The proposed system proved
its ability to detect FF domains in online mode with high detection accuracy (98.77%) compare with other algorithms, with low false positive and negative rates respectively. It is also proved a high level of performance. Additionally, the proposed adaptation of the algorithm enhanced and helped in the parameters customization
process
Cover Tree Bayesian Reinforcement Learning
This paper proposes an online tree-based Bayesian approach for reinforcement
learning. For inference, we employ a generalised context tree model. This
defines a distribution on multivariate Gaussian piecewise-linear models, which
can be updated in closed form. The tree structure itself is constructed using
the cover tree method, which remains efficient in high dimensional spaces. We
combine the model with Thompson sampling and approximate dynamic programming to
obtain effective exploration policies in unknown environments. The flexibility
and computational simplicity of the model render it suitable for many
reinforcement learning problems in continuous state spaces. We demonstrate this
in an experimental comparison with least squares policy iteration
Online Bin Covering with Limited Migration
Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years.
This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor beta: When an object o of size s(o) arrives, the decisions for objects of total size at most beta * s(o) may be revoked. Usually beta should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classical problems such as bin packing or makespan minimization. The dual of makespan minimization - the Santa Claus or machine covering problem - has also been studied, whereas the dual of bin packing - the bin covering problem - has not been looked at from such a perspective.
In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case - where only insertions are allowed - and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small epsilon). We therefore resolve the competitiveness of the bin covering problem with migration
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