arXiv subjects

Jayant Chandwani

Publications and source records attributed to Jayant Chandwani.

2 recordsLinked to original sources

arXiv2026

A Graph Matching Based Approach for the Multi-Depot Capacitated Vehicle Routing Problem

The Multi-Depot Capacitated Vehicle Routing Problem (MDCVRP) asks for minimum-cost delivery tours from several capacitated depots to a set of customers. Like most vehicle-routing variants it is NP-hard, so practical solvers must trade solution quality against speed. We revisit this trade-off through the lens of graph matching. Adapting a matching-based construction first developed for the Traveling Tournament Problem, we present two algorithms, Cluster-First and Match-First, that reduce routing to a sequence of minimum-weight matchings. This is more than a heuristic. We prove that for tours of up to two targets the matching formulation solves the MDCVRP exactly in polynomial time for any number of depots, and that both algorithms are constant-factor approximations, with a tight factor of two, in the structured regimes. This matching optimum coincides with the exact combinatorial-auction optimum, so the auction serves as a strong quality baseline. On instances of 1000 customers and 20 depots our methods match or slightly beat that baseline in tour length while running two to three orders of magnitude faster, in tens of milliseconds against tens of seconds, a scale at which exact and auction-based solvers become impractical. Because Cluster-First routes each depot independently, the approach also re-routes cheaply when new customers arrive.

cs.DS↗

arXiv2026

BLOSSOM: Block-wise Federated Learning Over Shared and Sparse Observed Modalities

Multimodal federated learning (FL) is essential for real-world applications such as autonomous systems and healthcare, where data is distributed across heterogeneous clients with varying and often missing modalities. However, most existing FL approaches assume uniform modality availability, limiting their applicability in practice. We introduce BLOSSOM, a task-agnostic framework for multimodal FL designed to operate under shared and sparsely observed modality conditions. BLOSSOM supports clients with arbitrary modality subsets and enables flexible sharing of model components. To address client and task heterogeneity, we propose a block-wise aggregation strategy that selectively aggregates shared components while keeping task-specific blocks private, enabling partial personalization. We evaluate BLOSSOM on multiple diverse multimodal datasets and analyse the effects of missing modalities and personalization. Our results show that block-wise personalization significantly improves performance, particularly in settings with severe modality sparsity. In modality-incomplete scenarios, BLOSSOM achieves an average performance gain of 18.7% over full-model aggregation, while in modality-exclusive settings the gain increases to 37.7%, highlighting the importance of block-wise learning for practical multimodal FL systems.

cs.LG↗