Dynamic Maintenance of Monotone Dynamic Programs and Applications

Dynamic programming (DP) is one of the fundamental paradigms in algorithm design. However, many DP algorithms have to fill in large DP tables, represented by two-dimensional arrays, which causes at least quadratic running times and space usages. This has led to the development of improved algorithms for special cases when the DPs satisfy additional properties like, e.g., the Monge property or total monotonicity. In this paper, we consider a new condition which assumes (among some other technical assumptions) that the rows of the DP table are monotone. Under this assumption, we introduce a novel data structure for computing (1+?)-approximate DP solutions in near-linear time and space in the static setting, and with polylogarithmic update times when the DP entries change dynamically. To the best of our knowledge, our new condition is incomparable to previous conditions and is the first which allows to derive dynamic algorithms based on existing DPs. Instead of using two-dimensional arrays to store the DP tables, we store the rows of the DP tables using monotone piecewise constant functions. This allows us to store length-n DP table rows with entries in [0,W] using only polylog(n,W) bits, and to perform operations, such as (min,+)-convolution or rounding, on these functions in polylogarithmic time. We further present several applications of our data structure. For bicriteria versions of k-balanced graph partitioning and simultaneous source location, we obtain the first dynamic algorithms with subpolynomial update times, as well as the first static algorithms using only near-linear time and space. Additionally, we obtain the currently fastest algorithm for fully dynamic knapsack

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Approximate Dynamic Programming using Halfspace Queries and Multiscale Monge Decomposition

We consider the problem of approximating a signal P with another signal F consisting of a few piecewise constant segments. This problem arises naturally in applications including databases (e.g., histogram construction), speech recognition, computational biology (e.g., denoising aCGH data) and many more. Specifically, let P = (P1, P2,..., Pn), Pi ∈ R for all i, be a signal and let C be a constant. Our goal is to find a function F: [n] → R which optimizes the following objective function: (0.1) min F n

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio