arXiv subjects

Mohit Garg

Publications and source records attributed to Mohit Garg.

At least 19 recordsLinked to original sources

arXiv2026

Online Connectivity Augmentation

The Connectivity Augmentation Problem (CAP) is a fundamental problem in fault-tolerant network design and has been extensively studied in the context of approximation algorithms. In this work, we consider CAP in the online setting: given a $k$-edge-connected graph $G$ and a set $L$ of additional edges over the vertices of $G$, called links, online requests arrive one by one, each specifying two vertices that need to be $(k+1)$-edge-connected. We start with the graph $G$ and progressively add links to serve these requests. More specifically, upon the arrival of a request $\{u,v\}$, we must immediately and irrevocably add zero or more links from $L$ to the graph so that $u$ and $v$ are $(k+1)$-edge-connected in the resulting augmented graph. The goal is to minimize the total number of links added, and we evaluate an algorithm's performance by its competitive ratio relative to an optimal offline solution. In this work, improving upon previous bounds, we obtain a tight competitive ratio for online CAP, along with other related results.

cs.DS↗

arXiv2026

Resilient AI Supercomputer Networking using MRC and SRv6

Tail latency dominates the performance of synchronous pretraining jobs when running at very large scales. We describe a three-pronged approach: (1) a new RDMA-based transport protocol, MRC, sprays across many paths and actively load-balances between them, eliminating the issue of flow collisions (2) the use of multi-plane Clos topologies to get the benefits of high switch radix and redundancy, allowing training clusters well over 100K GPUs to be built as two-tier topologies while increasing physical redundancy, and (3) the use of static source-routing using SRv6 to allow MRC the freedom to bypass failures by itself. We describe our experiences running MRC and static SRv6 routing in production in OpenAI and Microsoft's largest training clusters, where it has been used to train the latest frontier models. We demonstrate how MRC allows AI training jobs to ride out many network failures that previously would have interrupted training.

cs.NI↗

arXiv2026

LICA: Layered Image Composition Annotations for Graphic Design Research

We introduce LICA (Layered Image Composition Annotations), a large scale dataset of 1,550,244 multi-layer graphic design compositions designed to advance structured understanding and generation of graphic layouts. In addition to rendered PNG images, LICA represents each design as a hierarchical composition of typed components including text, image, vector, and group elements, each paired with rich per-element metadata such as spatial geometry, typographic attributes, opacity, and visibility. The dataset spans 20 design categories and 971,850 unique templates, providing broad coverage of real-world design structures. We further introduce graphic design video as a new and largely unexplored challenge for current vision-language models through 27,261 animated layouts annotated with per-component keyframes and motion parameters. Beyond scale, LICA establishes a new paradigm of research tasks for graphic design, enabling structured investigations into problems such as layer-aware inpainting, structured layout generation, controlled design editing, and temporally-aware generative modeling. By representing design as a system of compositional layers and relationships, the dataset supports research on models that operate directly on design structure rather than pixels alone.

cs.CV↗

arXiv2024

Efficient and Verified Continuous Double Auctions

Continuous double auctions are commonly used to match orders at currency, stock, and commodities exchanges. A verified implementation of continuous double auctions is a useful tool for market regulators as they give rise to automated checkers that are guaranteed to detect errors in the trade logs of an existing exchange if they contain trades that violate the matching rules. We provide an efficient and formally verified implementation of continuous double auctions that takes $O(n \log n)$ time to match $n$ orders. This improves an earlier $O(n^2)$ verified implementation. We also prove a matching $\Omega(n\log n)$ lower bound on the running time for continuous double auctions. Our new implementation takes only a couple of minutes to run on ten million randomly generated orders as opposed to a few days taken by the earlier implementation. Our new implementation gives rise to an efficient automatic checker. We use the Coq proof assistant for verifying our implementation and extracting a verified OCaml program. While using Coq's standard library implementation of red-black trees to obtain our improvement, we observed that its specification has serious gaps, which we fill in this work; this might be of independent interest.

cs.LO↗

arXiv2024

Double Auctions: Formalization and Automated Checkers

Double auctions are widely used in financial markets, such as those for stocks, derivatives, currencies, and commodities, to match demand and supply. Once all buyers and sellers have placed their trade requests, the exchange determines how these requests are to be matched. The two most common objectives for determining the matching are maximizing trade volume at a uniform price and maximizing trade volume through dynamic pricing. Prior research has primarily focused on single-quantity trade requests. In this work, we extend the framework to handle multiple-quantity trade requests and present fully formalized matching algorithms for double auctions, along with their correctness proofs. We establish new uniqueness theorems, enabling automatic detection of violations in exchange systems by comparing their output to that of a verified program. All proofs are formalized in the Coq Proof Assistant, and we extract verified OCaml and Haskell programs that could serve as a resource for exchanges and market regulators. We demonstrate the practical applicability of our work by running the verified program on real market data from an exchange to automatically check for violations in the exchange algorithm.

cs.LO↗

arXiv2024

A $5/4$-Approximation for Two-Edge Connectivity

The 2-Edge-Connected Spanning Subgraph problem (2ECSS) is among the most basic survivable network design problems: given an undirected and unweighted graph, the task is to find a spanning subgraph with the minimum number of edges that is 2-edge-connected (i.e., it remains connected after the removal of any single edge). 2ECSS is an NP-hard problem that has been extensively studied in the context of approximation algorithms. The best known approximation ratio for 2ECSS prior to this work was $1.3+\varepsilon$, for any constant $\varepsilon>0$ [Garg, Grandoni, Jabal-Ameli'23; Kobayashi, Noguchi'23]. In this paper, we present a 5/4-approximation algorithm. Our algorithm is also faster for small values of $\varepsilon$: its running time is $n^{O(1)}$ instead of $n^{O(1/\varepsilon)}$.

cs.DS↗

arXiv2024

Two-Edge Connectivity via Pac-Man Gluing

We study the 2-edge-connected spanning subgraph (2-ECSS) problem: Given a graph $G$, compute a connected subgraph $H$ of $G$ with the minimum number of edges such that $H$ is spanning, i.e., $V(H) = V(G)$, and $H$ is 2-edge-connected, i.e., $H$ remains connected upon the deletion of any single edge, if such an $H$ exists. The $2$-ECSS problem is known to be NP-hard. In this work, we provide a polynomial-time $(\frac 5 4 + \varepsilon)$-approximation for the problem for an arbitrarily small $\varepsilon>0$, improving the previous best approximation ratio of $\frac{13}{10}+\varepsilon$. Our improvement is based on two main innovations: First, we reduce solving the problem on general graphs to solving it on structured graphs with high vertex connectivity. This high vertex connectivity ensures the existence of a 4-matching across any bipartition of the vertex set with at least 10 vertices in each part. Second, we exploit this property in a later gluing step, where isolated 2-edge-connected components need to be merged without adding too many edges. Using the 4-matching property, we can repeatedly glue a huge component (containing at least 10 vertices) to other components. This step is reminiscent of the Pac-Man game, where a Pac-Man (a huge component) consumes all the dots (other components) as it moves through a maze. These two innovations lead to a significantly simpler algorithm and analysis for the gluing step compared to the previous best approximation algorithm, which required a long and tedious case analysis.

cs.DS↗

arXiv2024

The Exchange Problem

Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the matching are maximizing volume at a uniform price and maximizing volume with dynamic pricing. In this work, we study the algorithmic complexity of the problems arising from these matching tasks. We present a linear time algorithm for uniform price matching which is an improvement over the previous algorithms that take $O(n\log n)$ time to match $n$ requests. For dynamic price matching, we establish a lower bound of $Ω(n \log n)$ on the running time, thereby proving that the currently known best algorithm is time-optimal.

cs.DS↗

arXiv2024

Random-Order Online Independent Set of Intervals and Hyperrectangles

In the Maximum Independent Set of Hyperrectangles problem, we are given a set of $n$ (possibly overlapping) $d$-dimensional axis-aligned hyperrectangles, and the goal is to find a subset of non-overlapping hyperrectangles of maximum cardinality. For $d=1$, this corresponds to the classical Interval Scheduling problem, where a simple greedy algorithm returns an optimal solution. In the offline setting, for $d$-dimensional hyperrectangles, polynomial time $(\log n)^{O(d)}$-approximation algorithms are known. However, the problem becomes notably challenging in the online setting, where the input objects (hyperrectangles) appear one by one in an adversarial order, and on the arrival of an object, the algorithm needs to make an immediate and irrevocable decision whether or not to select the object while maintaining the feasibility. Even for interval scheduling, an $\Omega(n)$ lower bound is known on the competitive ratio. To circumvent these negative results, in this work, we study the online maximum independent set of axis-aligned hyperrectangles in the random-order arrival model, where the adversary specifies the set of input objects which then arrive in a uniformly random order. Starting from the prototypical secretary problem, the random-order model has received significant attention to study algorithms beyond the worst-case competitive analysis. Surprisingly, we show that the problem in the random-order model almost matches the best-known offline approximation guarantees, up to polylogarithmic factors. In particular, we give a simple $(\log n)^{O(d)}$-competitive algorithm for $d$-dimensional hyperrectangles in this model, which runs in $\tilde{O_d}(n)$ time. Our approach also yields $(\log n)^{O(d)}$-competitive algorithms in the random-order model for more general objects such as $d$-dimensional fat objects and ellipsoids. Furthermore, our guarantees hold with high probability.

cs.DS↗

arXiv2023

Empower Large Language Model to Perform Better on Industrial Domain-Specific Question Answering

Large Language Model (LLM) has gained popularity and achieved remarkable results in open-domain tasks, but its performance in real industrial domain-specific scenarios is average due to its lack of specific domain knowledge. This issue has attracted widespread attention, but there are few relevant benchmarks available. In this paper, we provide a benchmark Question Answering (QA) dataset named MSQA, centered around Microsoft products and IT technical problems encountered by customers. This dataset contains industry cloud-specific QA knowledge, an area not extensively covered in general LLMs, making it well-suited for evaluating methods aiming to enhance LLMs' domain-specific capabilities. In addition, we propose a new model interaction paradigm that can empower LLM to achieve better performance on domain-specific tasks where it is not proficient. Extensive experiments demonstrate that the approach following our method outperforms the commonly used LLM with retrieval methods. We make our source code and sample data available at: https://aka.ms/Microsoft_QA.

cs.CL↗

arXiv2023

Matching Augmentation via Simultaneous Contractions

We consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a $2$-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an approximation ratio of $13/8 = 1.625$ improving upon an earlier $5/3$-approximation. The improvement builds on a new $α$-approximation preserving reduction for any $α\geq 3/2$ from arbitrary MAP instances to well-structured instances that do not contain certain forbidden structures like parallel edges, small separators, and contractible subgraphs. We further introduce, as key ingredients, the technique of repeated simultaneous contractions and provide improved lower bounds for instances that cannot be contracted.

cs.DS↗

arXiv2023

Can listening to more neighbours help CAVs be faster and safer?

Connected Autonomous Vehicles (CAVs) are widely expected to improve traffic safety and efficiency by exploiting information from surrounding vehicles via V2V communication. A CAV typically adapts its speed based on information from the vehicle it follows. CAVs can also use information from vehicles further ahead within their communication range, and this results in improved traffic safety and efficiency. In mixed traffic scenarios, however, this may not always be possible due to the presence of human-driven vehicles that do not have communication capabilities. Furthermore, as wireless vehicular networks are unreliable, information from other vehicles can be delayed or lost, which brings more challenges for CAVs in utilizing information from multiple leading vehicles. A few studies have investigated the impact of CAVs where they use information from multiple leading vehicles on traffic safety and efficiency, but only in very limited scenarios (i.e., with a very small number of vehicles). In contrast, this paper investigates the impact of CAV car-following control based on multiple leading vehicles information on both mixed traffic safety and efficiency in realistic scenarios in terms of imperfect communication, vehicle modelling, and traffic scenario. Results show that exploiting information from multiple, rather than a single, leading vehicles in CAV controller design further improves both traffic safety and efficiency especially at high penetration rates. In addition to proper tuning of CAV controller parameters (control gains and time headways), the scale of the improvement depends on both market penetration rate (MPR) and communication reliability. A packet error rate (PER) of 70% leads to an increase in traffic efficiency by 4.18% (at 40% MPR) and 12.19% (at 70% MPR), compared to the simple single leading vehicle information based controller.

eess.SY↗

arXiv2022

Improved Approximation for Two-Edge-Connectivity

The basic goal of survivable network design is to construct low-cost networks which preserve a sufficient level of connectivity despite the failure or removal of a few nodes or edges. One of the most basic problems in this area is the $2$-Edge-Connected Spanning Subgraph problem (2-ECSS): given an undirected graph $G$, find a $2$-edge-connected spanning subgraph $H$ of $G$ with the minimum number of edges (in particular, $H$ remains connected after the removal of one arbitrary edge). 2-ECSS is NP-hard and the best-known (polynomial-time) approximation factor for this problem is $4/3$. Interestingly, this factor was achieved with drastically different techniques by [Hunkenschr{ö}der, Vempala and Vetta '00,'19] and [Seb{ö} and Vygen, '14]. In this paper we present an improved $\frac{118}{89}+ε<1.326$ approximation for 2-ECSS. The key ingredient in our approach (which might also be helpful in future work) is a reduction to a special type of structured graphs: our reduction preserves approximation factors up to $6/5$. While reducing to 2-vertex-connected graphs is trivial (and heavily used in prior work), our structured graphs are "almost" 3-vertex-connected: more precisely, given any 2-vertex-cut $\{u,v\}$ of a structured graph $G=(V,E)$, $G[V\setminus \{u,v\}]$ has exactly 2 connected components, one of which contains exactly one node of degree $2$ in $G$.

cs.DS↗

arXiv2022

The Design and Regulation of Exchanges: A Formal Approach

We use formal methods to specify, design, and monitor continuous double auctions, which are widely used to match buyers and sellers at exchanges of foreign currencies, stocks, and commodities. We identify three natural properties of such auctions and formally prove that these properties completely determine the input-output relationship. We then formally verify that a natural algorithm satisfies these properties. All definitions, theorems, and proofs are formalized in an interactive theorem prover. We extract a verified program of our algorithm to build an automated checker that is guaranteed to detect errors in the trade logs of exchanges if they generate transactions that violate any of the natural properties.

cs.LO↗

arXiv2021

Can Connected Autonomous Vehicles really improve mixed traffic efficiency in realistic scenarios?

Connected autonomous vehicles (CAVs) can supplement the information from their own sensors with information from surrounding CAVs for decision making and control. This has the potential to improve traffic efficiency. CAVs face additional challenges in their driving, however, when they interact with human-driven vehicles (HDVs) in mixed-traffic environments due to the uncertainty in human's driving behavior e.g. larger reaction times, perception errors, etc. While a lot of research has investigated the impact of CAVs on traffic safety and efficiency at different penetration rates, all have assumed either perfect communication or very simple scenarios with imperfect communication. In practice, the presence of communication delays and packet losses means that CAVs might receive only partial information from surrounding vehicles, and this can have detrimental effects on their performance. This paper investigates the impact of CAVs on traffic efficiency in realistic communication and road network scenarios (i.e. imperfect communication and large-scale road network). We analyze the effect of unreliable communication links on CAVs operation in mixed traffic with various penetration rates and evaluate traffic performance in congested traffic scenarios on a large-scale road network (the M50 motorway, in Ireland). Results show that CAVs can significantly improve traffic efficiency in congested traffic scenarios at high penetration rates. The scale of the improvement depends on communication reliability, with a packet drop rate of 70% leading to an increase in traffic congestion by 28.7% and 11.88% at 40% and 70% penetration rates respectively compared to perfect communication.

cs.DC↗

arXiv2018

Online Submodular Maximization: Beating 1/2 Made Simple

The Submodular Welfare Maximization problem (SWM) captures an important subclass of combinatorial auctions and has been studied extensively from both computational and economic perspectives. In particular, it has been studied in a natural online setting in which items arrive one-by-one and should be allocated irrevocably upon arrival. In this setting, it is well known that the greedy algorithm achieves a competitive ratio of 1/2, and recently Kapralov et al. (2013) showed that this ratio is optimal for the problem. Surprisingly, despite this impossibility result, Korula et al. (2015) were able to show that the same algorithm is 0.5052-competitive when the items arrive in a uniformly random order, but unfortunately, their proof is very long and involved. In this work, we present an (arguably) much simpler analysis that provides a slightly better guarantee of 0.5096-competitiveness for the greedy algorithm in the random-arrival model. Moreover, this analysis applies also to a generalization of online SWM in which the sets defining a (simple) partition matroid arrive online in a uniformly random order, and we would like to maximize a monotone submodular function subject to this matroid. Furthermore, for this more general problem, we prove an upper bound of 0.576 on the competitive ratio of the greedy algorithm, ruling out the possibility that the competitiveness of this natural algorithm matches the optimal offline approximation ratio of 1-1/e.

cs.DS↗

arXiv2018

Deterministic (1/2 + ε)-Approximation for Submodular Maximization over a Matroid

We study the problem of maximizing a monotone submodular function subject to a matroid constraint and present a deterministic algorithm that achieves (1/2 + ε)-approximation for the problem. This algorithm is the first deterministic algorithm known to improve over the 1/2-approximation ratio of the classical greedy algorithm proved by Nemhauser, Wolsely and Fisher in 1978.

cs.DS↗

arXiv2016

Set membership with non-adaptive bit probes

We consider the non-adaptive bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form "Is x in S?" by non-adaptively probing the bit vector at t places. Let s_N(m,n,t) be the minimum number of bits of storage needed for such a scheme. In this work, we show existence of non-adaptive and adaptive schemes for a range of t that improves an upper bound of Buhrman, Miltersen, Radhakrishnan and Srinivasan (2002) on s_N(m,n,t). For three non-adaptive probes, we improve the previous best lower bound on s_N(m,n,3) by Alon and Feige (2009).

cs.DS↗