arXiv subjects

David Aleman Espinosa

Publications and source records attributed to David Aleman Espinosa.

2 recordsLinked to original sources

arXiv2026

Approximation Algorithms for Norm-Budgeted Packing Problems

In recent years, much attention has been devoted to the study of optimization problems under norm-based objectives coming from the rich class of monotone, symmetric norms (and their generalizations). This work has however almost exclusively focused on covering problems, wherein one seeks to minimize the norm of the cost vector induced by a solution. We introduce and study the class of {\em norm-budgeted packing problems}, which are packing problems where the resource constraints underlying the packing problem are modeled via a {\em norm budget constraint} involving a {\em monotone, symmetric norm}. Formally, we have some elements with associated rewards and sizes, a downwards-closed collection of feasible solutions, and a budget $B$. Each solution induces a size vector, and the goal is to maximize the total reward subject to the norm-budget constraint $f(\text{size vector})\leq B$. The versatility of monotone, symmetric norms implies that a variety of classical packing problems can be captured under the umbrella of norm-budgeted packing problems. Moreover, the closure properties of monotone, symmetric norms, also enable one to encode multiple different norm-budget constraints via a single monotone, symmetric norm. We consider the norm-budgeted versions of a variety of canonical packing problems, including knapsack, matching, maximum-weight independent set in a $k$-set system, maximum generalized assignment problem (MaxGAP), and $k$-facility location, and develop a framework that allows us to obtain {\em constant-factor approximation guarantees} for these problems, and {\em PTASes for knapsack, and MaxGAP on identical and related machines}. We also develop constant-factor approximation algorithms for the {\em submodular} versions of some norm-budgeted packing problems, wherein the reward function is now specified by a monotone, submodular function.

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arXiv2024

Approximation Algorithms for Correlated Knapsack Orienteering

We consider the {\em correlated knapsack orienteering} (CSKO) problem: we are given a travel budget $B$, processing-time budget $W$, finite metric space $(V,d)$ with root $ρ\in V$, where each vertex is associated with a job with possibly correlated random size and random reward that become known only when the job completes. Random variables are independent across different vertices. The goal is to compute a $ρ$-rooted path of length at most $B$, in a possibly adaptive fashion, that maximizes the reward collected from jobs that are processed by time $W$. To our knowledge, CSKO has not been considered before, though prior work has considered the uncorrelated problem, {\em stochastic knapsack orienteering}, and {\em correlated orienteering}, which features only one budget constraint on the {\em sum} of travel-time and processing-times. We show that the {\em adaptivity gap of CSKO is not a constant, and is at least $Ω\bigl(\max\sqrt{\log{B}},\sqrt{\log\log{W}}\}\bigr)$}. Complementing this, we devise {\em non-adaptive} algorithms that obtain: (a) $O(\log\log W)$-approximation in quasi-polytime; and (b) $O(\log W)$-approximation in polytime. We obtain similar guarantees for CSKO with cancellations, wherein a job can be cancelled before its completion time, foregoing its reward. We also consider the special case of CSKO, wherein job sizes are weighted Bernoulli distributions, and more generally where the distributions are supported on at most two points (2-CSKO). Although weighted Bernoulli distributions suffice to yield an $Ω(\sqrt{\log\log B})$ adaptivity-gap lower bound for (uncorrelated) {\em stochastic orienteering}, we show that they are easy instances for CSKO. We develop non-adaptive algorithms that achieve $O(1)$-approximation in polytime for weighted Bernoulli distributions, and in $(n+\log B)^{O(\log W)}$-time for the more general case of 2-CSKO.

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