arXiv subjects

Arghya Chakraborty

Publications and source records attributed to Arghya Chakraborty.

4 recordsLinked to original sources

arXiv2026

Arrival-Time Incentive Compatibility in Random Order Online Bipartite Matching

In this work we initiate the study of competitive algorithms with arrival-time incentive compatibility for random-order online bipartite matching in settings where the users care only about receiving service (matched vs. unmatched) and not which offline resource serves them, while the platform's objective is to maximize total matching reward. This captures applications such as ride-sharing where the users primarily care about being matched to a ride while the platform internalizes the cost of dispatching a distant driver; dispatching homogeneous service requests to heterogeneous servers (cloud/edge routing); and assigning customer requests to a pool of providers with different flexibility (e.g., English-only vs. bilingual agents). Our main question is: \textit{Is constant-competitive matching possible for incentive-compatible, random-order edge-weighted matching on complete bipartite graphs?} Motivated by the LP-based treatment of incentive compatibility in the classical secretary problem by Buchbinder et al., we impose a constraint that the ex ante probability of selection is equalized across all arrival positions. We answer our main question in the affirmative and propose the first constant-competitive algorithm for incentive compatible edge-weighted random-order online matching on complete bipartite graphs. The competitive ratio of our algorithm is parameterized by the imbalance factor $k := n/m$ -- where $n$ and $m$ are the numbers of online and offline nodes, respectively, and $k$ is a positive integer. In particular, we obtain a competitive guarantee of the form $c_k - O(1/\sqrt{m})$ where $c_1 \approx 0.162$ and $c_k \to 0.02308\ldots$ as $k \to \infty$. We also present algorithms with strictly improved competitive ratio of $\approx 0.07 + O(1/m)$ for the binary-weighted case ($0$-$1$ rewards).

cs.GT↗

arXiv2025

Optimal Online Bipartite Matching in Degree-2 Graphs

Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of $1-\frac{1}{e}$. In this work, we study classes of graphs where the online degree is restricted to $2$. As expected, one can achieve a competitive ratio of better than $1-\frac{1}{e}$ in both the deterministic fractional and randomized integral cases, but surprisingly, these ratios are not the same. It was already known that for fractional matching, a $0.75$ competitive ratio algorithm is optimal. We show that the folklore \textsc{Half-Half} algorithm achieves a competitive ratio of $η\approx 0.717772\dots$ and more surprisingly, show that this is optimal by giving a matching lower-bound. This yields a separation between the two problems: deterministic fractional and randomized integral, showing that it is impossible to obtain a perfect rounding scheme.

cs.DS↗

arXiv2025

Exploring membership and variability in NGC 7419: An open cluster rich in super giants and Be type stars

NGC 7419 is a young open cluster notable for hosting five Red Supergiants and a high abundance of Classical Be (CBe) stars. CBe stars are main sequence non-supergiant B-type stars, which exhibit or have exhibited Balmer line emissions in their spectra. We perform a membership analysis using Gaia DR3 data and machine learning techniques like Gaussian Mixture Models (GMM) and Random Forest (RF) and determine the cluster's mean distance to be ${3.6^{+1.0}_{-0.6}}$ kpc. We identify 499 Gaia-based members with a mass above $\sim$ 1.2 M$_\odot$, and estimate the cluster's age to be $21.1 ^{+1.6}_{-0.6}$ Myr. Using our revised $Hα$ excess-based analysis, we find 42 CBe stars containing many known CBe stars, bringing the total number of CBe stars in NGC 7419 to 49 and the fraction of CBe to (B+CBe) members to 12.7%. We investigate the variability of the candidate members from ZTF and NEOWISE data using Standard Deviation, Median Absolute Deviation, and Stetson Index (J), and their periodicity using the Generalized Lomb Scargle Periodogram variability. We find that 66% of CBe stars are variable: 23% show periodic signals, typical of pulsation/rotation, 41% display variability characteristic of disk dynamics or binarity, and 14% exhibit long-term changes, consistent with disk dissipation/formation. We also find that all pulsating CBe stars are early-type, while 50% of stars with long-term variations are early-type, and the other 50% are mid-type. Our results agree with previous findings in the literature and confirm that CBe stars display variability through multiple mechanisms across different timescales.

astro-ph.SR↗

arXiv2023

Online facility location with weights and congestion

The classic online facility location problem deals with finding the optimal set of facilities in an online fashion when demand requests arrive one at a time and facilities need to be opened to service these requests. In this work, we study two variants of the online facility location problem; (1) weighted requests and (2) congestion. Both of these variants are motivated by their applications to real life scenarios and the previously known results on online facility location cannot be directly adapted to analyse them. Weighted requests: In this variant, each demand request is a pair $(x,w)$ where $x$ is the standard location of the demand while $w$ is the corresponding weight of the request. The cost of servicing request $(x,w)$ at facility $F$ is $w\cdot d(x,F)$. For this variant, given $n$ requests, we present an online algorithm attaining a competitive ratio of $\mathcal{O}(\log n)$ in the secretarial model for the weighted requests and show that it is optimal. Congestion: The congestion variant considers the case when there is an additional congestion cost that grows with the number of requests served by each facility. For this variant, when the congestion cost is a monomial, we show that there exists an algorithm attaining a constant competitive ratio. This constant is a function of the exponent of the monomial and the facility opening cost but independent of the number of requests.

cs.DS↗