Search arXivSearch

arXiv · 2409.09623

Multi-Slot Tag Assignment Problem in Billboard Advertisement

Abstract

Nowadays, billboard advertising has emerged as an effective advertising technique due to higher returns on investment. Given a set of selected slots and tags, how to effectively assign the tags to the slots remains an important question. In this paper, we study the problem of assigning tags to the slots such that the number of tags for which influence demand of each zone is satisfied gets maximized. Formally, we call this problem the Multi-Slot Tag Assignment Problem. The input to the problem is a geographical region partitioned into several zones, a set of selected tags and slots, a trajectory, a billboard database, and the influence demand for every tag for each zone. The task here is to find out the assignment of tags to the slots, such the number of tags for which the zonal influence demand is satisfied is maximized. We show that the problem is NP-hard, and we propose an efficient approximation algorithm to solve this problem. A time and space complexity analysis of the proposed methodology has been done. The proposed methodology has been implemented with real-life datasets, and a number of experiments have been carried out to show the effectiveness and efficiency of the proposed approach. The obtained results have been compared with the baseline methods, and we observe that the proposed approach leads to a number of tags whose zonal influence demand is satisfied.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dildar Ali, Suman Banerjee, Yamuna Prasad. 2024-09-15. Multi-Slot Tag Assignment Problem in Billboard Advertisement. https://arxiv.org/abs/2409.09623

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

The Marked Edge Walk: A Novel MCMC Algorithm for Sampling of Graph Partitions

Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans modeled as a graph partitioning problem. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest Recombination (MFR) have strong preferences for distributions related to the spanning tree measure. In this paper we introduce the Marked Edge Walk (MEW), a novel Markov chain proposal for sampling from the space of graph partitions. The walk operates on the space of spanning trees with marked edges, allowing for calculable transition probabilities for use in the Metropolis-Hastings algorithm. Empirical results on real-world dual graphs show convergence under a broad class of target distributions less constrained by spanning tree counts, including policy-based distributions, such as competitiveness on New Hampshire that are independent of spanning trees, and compactness and partisan symmetry distributions on New Hampshire and Texas that, while related to spanning trees, can now be properly targeted with a smaller degree of spanning tree bias, which represents an advancement in flexible ensemble generation.

cs.DS

The Price of Privacy For Approximating Max-CSP

We study approximation algorithms for Maximum Constraint Satisfaction Problems (Max-CSPs) under differential privacy (DP) where the constraints are considered sensitive data. Information-theoretically, we aim to classify the best approximation ratios possible for a given privacy budget $\varepsilon$. In the high-privacy regime ($\varepsilon \ll 1$), we show that any $\varepsilon$-DP algorithm cannot beat a random assignment by more than $O(\varepsilon)$ in the approximation ratio. We devise a polynomial-time algorithm which matches this barrier under the assumptions that the instances are bounded-degree and triangle-free. Finally, we show that one or both of these assumptions can be removed for specific CSPs--such as Max-Cut or Max $k$-XOR--albeit at the cost of computational efficiency.

cs.DS

Distributed Santa Claus via Global Rounding

In this paper, we initiate the study of a new class of problems in the CONGEST model: Mixed packing and covering linear programs (LP). Previously, the design of optimization algorithms in the distributed setting was heavily focused on solving linear programs with either packing or covering constraints. We are the first to explore the class of linear programs with both packing and covering constraints by providing a general-purpose CONGEST solver for such LPs and by studying the sequentially well-studied Santa Claus problem as a central representative. This NP-hard problem can be modeled as a bipartite graph of children and gifts where an edge indicates that a child desires a gift. The goal is to assign the gifts to the children such that the least happy child is as happy as possible. Even though this is a well-studied problem in the sequential setting, we provide the first results in the distributed setting. In particular, we show that the complexity of computing an $\mathcal{O}(\log n/\log \log n)$-approximation is $\widehat Θ(\sqrt n+D)$ rounds, where our $\widetildeΩ(\sqrt n+D)$-round lower bound even holds for any approximation.

cs.DS