arXiv subjects

Anders Wikum

Publications and source records attributed to Anders Wikum.

5 recordsLinked to original sources

arXiv2025

Optimal Rounding for Two-Stage Bipartite Matching

We study two-stage bipartite matching, in which the edges of a bipartite graph on vertices $(B_1 \cup B_2, I)$ are revealed in two batches. In stage one, a matching must be selected from among revealed edges $E \subseteq B_1 \times I$. In stage two, edges $E^\theta \subseteq B_2 \times I$ are sampled from a known distribution, and a second matching must be selected between $B_2$ and unmatched vertices in $I$. The objective is to maximize the total weight of the combined matching. We design polynomial-time approximations to the optimum online algorithm, achieving guarantees of $7/8$ for vertex-weighted graphs and $2\sqrt{2}-2 \approx 0.828$ for edge-weighted graphs under arbitrary distributions. Both approximation ratios match known upper bounds on the integrality gap of the natural fractional relaxation, improving upon the best-known approximation of 0.767 by Feng, Niazadeh, and Saberi for unweighted graphs whose second batch consists of independently arriving nodes. Our results are obtained via an algorithm that rounds a fractional matching revealed in two stages, aiming to match offline nodes (respectively, edges) with probability proportional to their fractional weights, up to a constant-factor loss. We leverage negative association (NA) among offline node availabilities -- a property induced by dependent rounding -- to derive new lower bounds on the expected size of the maximum weight matching in random graphs where one side is realized via NA binary random variables. Moreover, we extend these results to settings where we have only sample access to the distribution. In particular, $\text{poly}(n,\epsilon^{-1})$ samples suffice to obtain an additive loss of $\epsilon$ in the approximation ratio for the vertex-weighted problem; a similar bound holds for the edge-weighted problem with an additional (unavoidable) dependence on the scale of edge weights.

cs.DS↗

arXiv2025

Algorithms with Calibrated Machine Learning Predictions

The field of algorithms with predictions incorporates machine learning advice in the design of online algorithms to improve real-world performance. A central consideration is the extent to which predictions can be trusted -- while existing approaches often require users to specify an aggregate trust level, modern machine learning models can provide estimates of prediction-level uncertainty. In this paper, we propose calibration as a principled and practical tool to bridge this gap, demonstrating the benefits of calibrated advice through two case studies: the ski rental and online job scheduling problems. For ski rental, we design an algorithm that achieves near-optimal prediction-dependent performance and prove that, in high-variance settings, calibrated advice offers more effective guidance than alternative methods for uncertainty quantification. For job scheduling, we demonstrate that using a calibrated predictor leads to significant performance improvements over existing methods. Evaluations on real-world data validate our theoretical findings, highlighting the practical impact of calibration for algorithms with predictions.

stat.ML↗

arXiv2024

LLMs for Cold-Start Cutting Plane Separator Configuration

Mixed integer linear programming (MILP) solvers expose hundreds of parameters that have an outsized impact on performance but are difficult to configure for all but expert users. Existing machine learning (ML) approaches require training on thousands of related instances, generalize poorly and can be difficult to integrate into existing solver workflows. We propose a large language model (LLM)-based framework that configures cutting plane separators using problem descriptions and solver-specific separator summaries. To reduce variance in LLM outputs, we introduce an ensembling strategy that clusters and aggregates candidate configurations into a small portfolio of high-performing configurations. Our method requires no custom solver interface, generates configurations in seconds via simple API calls, and requires solving only a small number of instances. Extensive experiments on standard synthetic and real-world MILPs show our approach matches or outperforms state-of-the-art configuration methods with a fraction of the data and computation.

cs.LG↗

arXiv2024

MAGNOLIA: Matching Algorithms via GNNs for Online Value-to-go Approximation

Online Bayesian bipartite matching is a central problem in digital marketplaces and exchanges, including advertising, crowdsourcing, ridesharing, and kidney exchange. We introduce a graph neural network (GNN) approach that emulates the problem's combinatorially-complex optimal online algorithm, which selects actions (e.g., which nodes to match) by computing each action's value-to-go (VTG) -- the expected weight of the final matching if the algorithm takes that action, then acts optimally in the future. We train a GNN to estimate VTG and show empirically that this GNN returns high-weight matchings across a variety of tasks. Moreover, we identify a common family of graph distributions in spatial crowdsourcing applications, such as rideshare, under which VTG can be efficiently approximated by aggregating information within local neighborhoods in the graphs. This structure matches the local behavior of GNNs, providing theoretical justification for our approach.

cs.LG↗

arXiv2020

A Stochastic Model for Electric Scooter Systems

Electric scooters are becoming immensely popular across the world as a means of reliable transportation around many cities. As these e-scooters rely on batteries, it is important to understand how many of these e-scooters have enough battery life to transport riders and when these e-scooters might require a battery replacement. To this end, we develop the first stochastic model to capture the battery life dynamics of e-scooters of a large scooter network. In our model, we assume that e-scooter batteries are removable and replaced by agents called swappers. Thus, to gain some insight about the large scale dynamics of the system, we prove a mean field limit theorem and a functional central limit theorem for the fraction of e-scooters that lie in a particular interval of battery life. Exploiting the mean field limit and the functional central limit theorems, we develop an algorithm for determining the number of swappers that are needed to guarantee levels of probabilistic performance of the system. Finally, we show through a stochastic simulation and real data that our stochastic model captures the relevant dynamics.

math.PR↗