arXiv subjects

Aditya Anand

Publications and source records attributed to Aditya Anand.

At least 19 recordsLinked to original sources

arXiv2026

Approximating Minimum Spanning Trees in Metrics under Semi-Random Corruptions

We study the problem of finding minimum spanning trees in semi-random corrupted metrics. In this problem proposed by Bateni, Dharangutte, Jayaram, and Wang (COLT'24), we start with a metric space $\mathcal{M} = (X, d)$. The adversary independently corrupts each pairwise distance with probability $p$. The algorithm only observes these possibly corrupted distances and must output a spanning tree whose expected cost (in the true metric) is multiplicatively close to the minimum spanning tree cost. Prior work showed that losing a factor of $Ω(\log n)$ is necessary, even if the algorithm may adaptively select $O(n/\log n)$ points and probe the true distances between them. However, no upper bounds were known. We study three regimes based on whether the adversary can only increase, decrease, or arbitrarily change the corrupted distances. We show the following: (1) In the increase-only setting, we give a polynomial-time $O(1)$-approximation algorithm for any constant $0 \le p < 1$. (2) In the decrease-only setting, we give an $O(\log n)$-approximation algorithm for any constant $0 \le p < 1$. Additionally, we show an $O(\log^4 n)$-approximation algorithm that runs in quasi-polynomial time $n^{O(\log n)}$, for any constant $p \leq 0.1$. Moreover, we show that a polynomial-time algorithm computing an $n^{1/3-\varepsilon}$-approximation is unlikely to exist. (3) In the general setting, where the adversary can both increase and decrease distances, we show an $O(\log n)$-approximation algorithm for every $0 \leq p < \frac{1}{4}$. Further, we show that no $o(n)$-approximation is possible for $\frac{1}{2} \leq p < 1$. Our algorithms answer the main open question in Bateni et al.'s work; moreover, the $O(\log n)$-approximations in the latter two settings are information-theoretically optimal.

cs.DS↗

arXiv2026

Local Important Separators with Applications to Unbreakable Decomposition and Multicut

We present the first local FPT algorithm for finding important separators: Given an undirected graph $G$ with $n$ vertices and $m$ edges, vertices $s,t$ and parameters $k$ and $ν$, we can enumerate all $s$-$t$ important separators of size at most $k$ and volume at most $ν$ in time $\tilde{O}(ν2^{O(k)})$. Known approaches spend either $Ω(m)$ time (not local) or $ν^{Ω(k)}$ time (not FPT). Using this local algorithm, we show the following applications. (1) The first is an improved construction of unbreakable decomposition, a powerful generalization of tree decompositions. For any $k$, we can compute a $(5k,k)$-unbreakable decomposition with adhesion $4k$ in $\tilde{O}(k^{O(k)}m)$ time. This strictly subsumes the result of Anand, Lee, Li, Long, and Saranurak (SODA 2025) and is faster than the recent $O(k^{O(k^2)}m)$-time algorithm by Korhonen (STOC 2025) when $k = ω\Bigl(\sqrt{\frac{\log \log n}{\log \log \log n}}\Bigr)$. Our algorithm is also simpler than that of Korhonen (STOC 2025). (2) We give a near-linear time algorithm for single-sink important separators. For any sink $t$, we can list all $v$-$t$ important separators of size at most $k$ across all $v \in V(G)$ in time $\tilde{O}(2^{O(k)}m)$. Known approaches trivially compute $v$-$t$ important separators for each $v$, taking $Ω(4^k k mn)$ time. (3) Using the above result on single-sink important separators, we speed up undirected shadow removal and give the first almost-linear time FPT algorithm for Edge Multicut.

cs.DS↗

arXiv2026

Greedy Region Growing: Improved Approximations for Cutwidth, Pathwidth, Flow-Expander Decomposition, and More

We give a new rounding technique for spreading-metric linear programs, called Greedy Region Growing, which adapts the classical technique of region growing to min-max graph layout problems and flow-expander decomposition. Using this technique, we obtain state-of-the-art approximation algorithms for several fundamental problems. (1) An $O(\log n)$-approximation for Cutwidth and Pathwidth, improving upon the previous bound of $O(\log n\exp(O(\sqrt{\log\log n})))$ due to Bansal, Katzelnick, and Schwartz (FOCS 2024). This matches the $Ω(\log n)$ integrality gap of the standard LP relaxations. (2) An $O(\log n)$-approximation for their directed analogues, Minimum Storage and Minimum Register Sufficiency on directed acyclic graphs, improving the previous bound of $O(\log^{3/2} n)$. (3) A $ϕ$-flow-expander decomposition that cuts at most an $O(ϕ\log n\log\log n)$ fraction of the edges. This improves the $O(ϕ\log n\exp(O(\sqrt{\log\log n})))$ bound of Bansal, Jambulapati, and Saranurak (ICALP 2026), and is within an $O(\log\log n)$ factor of the graph-theoretic lower bound. The vertex version of our algorithm also gives an $O(\log n)$-approximation for Treedepth. In particular, our results answer several open problems of Bansal, Katzelnick, and Schwartz (FOCS 2024). Technically, we also solve the conceptual question raised by their work: our technique shows how to adapt Seymour recursion to min-max objectives, and constructs $O(1)$-weak local partitions in spreading metrics.

cs.DS↗

arXiv2026

Socially Fair Clustering: Parameterized Approximation and Local Search

We study the Socially Fair Clustering problem introduced by Abbasi, Bhaskara, and Venkatasubramanian (2021) and Ghadiri, Samadi, and Vempala (2021), along with its extension, the $(p,q)$-Socially Fair Clustering problem. This problem generalizes $k$-medians and $k$-means to settings where data points are partitioned into $\ell$ groups, and the goal is to find a fair clustering that is simultaneously good for all groups. We present several algorithms for this problem. For $\ell_p$-Socially Fair Clustering, we give the first constant-factor FPT-approximation parameterized by the number of groups $\ell$, resolving the open question raised by Ghadiri, Singh, and Vempala (2022). Our main ingredient is a new algorithm for closing additional centers in parameterized time inspired by local search. We then turn to the more general $(p,q)$-Socially Fair Clustering problem. The known algorithm for this problem, proposed by Chlamtáč, Makarychev, and Vakilian (2022) achieves a very good approximation but is complex, slow and difficult to implement. We analyze the performance of a simple local search algorithm and show that it provides an $O(q)$ approximation in the worst case. Finally, we design approximation algorithms for the facility location variant of the problem, where the number of facilities (centers) is not fixed in advance, and opening each facility incurs an opening cost. Unlike in previous work, we do not assume these opening costs are the same for all groups.

cs.DS↗

arXiv2026

Spectral Dual Fitting for $k$-Means

We give a new dual fitting algorithm which gives improved approximation ratios of $3+\ln 2 + ε (\approx 3.694)$ and $4.9+ε$ for $k$-Means in (high-dimensional) Euclidean and general metrics respectively, improving upon the previously known ratios of $4+ε$ [Charikar, Cohen-Addad, Gao, Grandoni, Lee, and van Wijland STOC'26] and $5+ε$ [Byrka, Guo, Hu, Li, Wan, Wang FOCS'26], resp. In particular, our result for Euclidean $k$-Means breaks the hardness barrier of $1+8/e\approx 3.94$ for Metric $k$-Means. Prior to our work, no such separation between general and Euclidean metrics was known for $k$-Median, $k$-Means, or Facility Location in terms of their approximability. Unlike prior dual fitting approaches for $k$-Means, our new dual fitting algorithm tightly accounts for dual payments while still facilitating an effective dual feasibility analysis. We introduce a new framework that uses spectral analysis for determining the approximation factor of our algorithm.

cs.DS↗

arXiv2026

Med-CAM: Minimal Evidence for Explaining Medical Decision Making

Reliable and interpretable decision-making is essential in medical imaging, where diagnostic outcomes directly influence patient care. Despite advances in deep learning, most medical AI systems operate as opaque black boxes, providing little insight into why a particular diagnosis was reached. In this paper, we introduce Med-CAM, a framework for generating minimal and sharp maps as evidence-based explanations for Medical decision making via Classifier Activation Matching. Med-CAM trains a segmentation network from scratch to produce a mask that highlights the minimal evidence critical to model's decision for any seen or unseen image. This ensures that the explanation is both faithful to the network's behaviour and interpretable to clinicians. Experiments show, unlike prior spatial explanation methods, such as Grad-CAM and attention maps, which yield only fuzzy regions of relative importance, Med-CAM with its superior spatial awareness to shapes, textures, and boundaries, delivers conclusive, evidence-based explanations that faithfully replicate the model's prediction for any given image. By explicitly constraining explanations to be compact, consistent with model activations, and diagnostic alignment, Med-CAM advances transparent AI to foster clinician understanding and trust in high-stakes medical applications such as pathology and radiology.

cs.CV↗

arXiv2025

Complexity of Local Search for CSPs Parameterized by Constraint Difference

In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible subset $S$ of a universe $U$, the new input consists of a current solution $P$ (not necessarily feasible) as well as an ordinary input for the problem. Given the existence of a feasible solution $S^*$, the goal is to find a feasible solution as good as $S^*$ in parameterized time $f(k) \cdot n^{O(1)}$, where $k$ denotes the distance $|PΔS^*|$. This model generalizes numerous classical parameterized optimization problems whose parameter $k$ is the minimum number of elements removed from $U$ to make it feasible, which corresponds to the case $P = U$. We apply this model to widely studied Constraint Satisfaction Problems (CSPs), where $U$ is the set of constraints, and a subset $U'$ of constraints is feasible if there is an assignment to the variables satisfying all constraints in $U'$. We give a complete characterization of the parameterized complexity of all boolean-alphabet symmetric CSPs, where the predicate's acceptance depends on the number of true literals.

cs.DS↗

arXiv2025

EXP-CAM: Explanation Generation and Circuit Discovery Using Classifier Activation Matching

Machine learning models, by virtue of training, learn a large repertoire of decision rules for any given input, and any one of these may suffice to justify a prediction. However, in high-dimensional input spaces, such rules are difficult to identify and interpret. In this paper, we introduce EXP-CAM: an explanation generation and circuit discovery approach using Classifier Activation Matching. EXP-CAM can generate minimal and faithful explanations for the decisions of pre-trained image classifiers that not only preserve the model's decision but are also concise and human-readable. We aim to identify minimal explanations that not only preserve the model's decision but are also concise and human-readable. To achieve this, we train a lightweight auto-encoder to produce binary masks that learns to highlight the decision-wise critical regions of an image while discarding irrelevant background. The training objective integrates activation alignment across multiple layers, consistency at the output label, priors that encourage sparsity, and compactness, along with a robustness constraint that enforces faithfulness. The minimal explanations so generated also lead us to mechanistically interpreting the model internals. In this regard we also introduce a circuit readout procedure wherein using the explanation's forward pass and gradients, we identify active channels and construct a channel-level graph, scoring inter-layer edges by ingress weight magnitude times source activation and feature-to-class links by classifier weight magnitude times feature activation. Together, these contributions provide a practical bridge between minimal input-level explanations and a mechanistic understanding of the internal computations driving model decisions.

cs.LG↗

arXiv2025

Activation Matching for Explanation Generation

In this paper we introduce an activation-matching--based approach to generate minimal, faithful explanations for the decision-making of a pretrained classifier on any given image. Given an input image $x$ and a frozen model $f$, we train a lightweight autoencoder to output a binary mask $m$ such that the explanation $e = m \odot x$ preserves both the model's prediction and the intermediate activations of $x$. Our objective combines: (i) multi-layer activation matching with KL divergence to align distributions and cross-entropy to retain the top-1 label for both the image and the explanation; (ii) mask priors -- L1 area for minimality, a binarization penalty for crisp 0/1 masks, and total variation for compactness; and (iii) abductive constraints for faithfulness and necessity. Together, these objectives yield small, human-interpretable masks that retain classifier behavior while discarding irrelevant input regions, providing practical and faithful minimalist explanations for the decision making of the underlying model.

cs.CV↗

arXiv2025

A Surrogate Model for the Forward Design of Multi-layered Metasurface-based Radar Absorbing Structures

Metasurface-based radar absorbing structures (RAS) are highly preferred for applications like stealth technology, electromagnetic (EM) shielding, etc. due to their capability to achieve frequency selective absorption characteristics with minimal thickness and reduced weight penalty. However, the conventional approach for the EM design and optimization of these structures relies on forward simulations, using full wave simulation tools, to predict the electromagnetic (EM) response of candidate meta atoms. This process is computationally intensive, extremely time consuming and requires exploration of large design spaces. To overcome this challenge, we propose a surrogate model that significantly accelerates the prediction of EM responses of multi-layered metasurface-based RAS. A convolutional neural network (CNN) based architecture with Huber loss function has been employed to estimate the reflection characteristics of the RAS model. The proposed model achieved a cosine similarity of 99.9% and a mean square error of 0.001 within 1000 epochs of training. The efficiency of the model has been established via full wave simulations as well as experiment where it demonstrated significant reduction in computational time while maintaining high predictive accuracy.

cs.CV↗

arXiv2025

All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs

Given a directed graph $G$ with $n$ vertices and $m$ edges, a parameter $k$ and two disjoint subsets $S,T \subseteq V(G)$, we show that the number of all-subsets important separators, which is the number of $A$-$B$ important vertex separators of size at most $k$ over all $A \subseteq S$ and $B \subseteq T$, is at most $β(|S|, |T|, k) = 4^k {|S| \choose \leq k} {|T| \choose \leq 2k}$, where ${x \choose \leq c} = \sum_{i = 1}^c {x \choose i}$, and that they can be enumerated in time $O(β(|S|,|T|,k)k^2(m+n))$. This is a generalization of the folklore result stating that the number of $A$-$B$ important separators for two fixed sets $A$ and $B$ is at most $4^k$ (first implicitly shown by Chen, Liu and Lu Algorithmica '09). From this result, we obtain the following applications: We give a construction for detection sets and sample sets in directed graphs, generalizing the results of Kleinberg (Internet Mathematics' 03) and Feige and Mahdian (STOC' 06) to directed graphs. Via our new sample sets, we give the first FPT algorithm for finding balanced separators in directed graphs parameterized by $k$, the size of the separator. Our algorithm runs in time $2^{O(k)} (m + n)$. We also give a $O({\sqrt{\log k}})$ approximation algorithm for the same problem. Finally, we present new results on vertex sparsifiers for preserving small cuts.

cs.DS↗

arXiv2025

Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT

This paper studies complete $k$-Constraint Satisfaction Problems (CSPs), where an $n$-variable instance has exactly one nontrivial constraint for each subset of $k$ variables, i.e., it has $\binom{n}{k}$ constraints. A recent work started a systematic study of complete $k$-CSPs [Anand, Lee, Sharma, SODA'25], and showed a quasi-polynomial time algorithm that decides if there is an assignment satisfying all the constraints of any complete Boolean-alphabet $k$-CSP, algorithmically separating complete instances from dense instances. The tractability of this decision problem is necessary for any nontrivial (multiplicative) approximation for the minimization version, whose goal is to minimize the number of violated constraints. The same paper raised the question of whether it is possible to obtain nontrivial approximation algorithms for complete Min-$k$-CSPs with $k \geq 3$. In this work, we make progress in this direction and show a quasi-polynomial time $\text{polylog}(n)$-approximation to Min-NAE-3-SAT on complete instances, which asks to minimize the number of $3$-clauses where all the three literals equal the same bit. To the best of our knowledge, this is the first known example of a CSP whose decision version is NP-Hard in general (and dense) instances while admitting a $\text{polylog}(n)$-approximation in complete instances. Our algorithm presents a new iterative framework for rounding a solution from the Sherali-Adams hierarchy, where each iteration interleaves the two well-known rounding tools: the conditioning procedure, in order to almost fix many variables, and the thresholding procedure, in order to completely fix them. Finally, we improve the running time of the decision algorithms of Anand, Lee, and Sharma and show a simple algorithm that decides any complete Boolean-alphabet $k$-CSP in polynomial time.

cs.DS↗

arXiv2024

Deterministic Edge Connectivity and Max Flow using Subquadratic Cut Queries

We give the first deterministic algorithm that makes sub-quadratic queries to find the global min-cut of a simple graph in the cut query model. Given an $n$-vertex graph $G$, our algorithm makes $\widetilde{O}(n^{5/3})$ queries to compute the global min-cut in $G$. As a key ingredient, we also show an algorithm for finding $s$-$t$ max-flows of size $\widetilde{O}(n)$ in $\widetilde{O}(n^{5/3})$ queries. We also show efficient cut-query implementations of versions of expander decomposition and isolating cuts, which may be of independent interest.

cs.DS↗

arXiv2024

Min-CSPs on Complete Instances

Given a fixed arity $k \geq 2$, Min-$k$-CSP on complete instances involves a set of $n$ variables $V$ and one nontrivial constraint for every $k$-subset of variables (so there are $\binom{n}{k}$ constraints). The goal is to find an assignment that minimizes unsatisfied constraints. Unlike Max-$k$-CSP that admits a PTAS on dense or expanding instances, the approximability of Min-$k$-CSP is less understood. For some CSPs like Min-$k$-SAT, there's an approximation-preserving reduction from general to dense instances, making complete instances unique for potential new techniques. This paper initiates a study of Min-$k$-CSPs on complete instances. We present an $O(1)$-approximation algorithm for Min-2-SAT on complete instances, the minimization version of Max-2-SAT. Since $O(1)$-approximation on dense or expanding instances refutes the Unique Games Conjecture, it shows a strict separation between complete and dense/expanding instances. Then we study the decision versions of CSPs, aiming to satisfy all constraints; which is necessary for any nontrivial approximation. Our second main result is a quasi-polynomial time algorithm for every Boolean $k$-CSP on complete instances, including $k$-SAT. We provide additional algorithmic and hardness results for CSPs with larger alphabets, characterizing (arity, alphabet size) pairs that admit a quasi-polynomial time algorithm on complete instances.

cs.DS↗

arXiv2024

Unbreakable Decomposition in Close-to-Linear Time

Unbreakable decomposition, introduced by Cygan et al. (SICOMP'19) and Cygan et al. (TALG'20), has proven to be one of the most powerful tools for parameterized graph cut problems in recent years. Unfortunately, all known constructions require at least $Ω_k\left(mn^2\right)$ time, given an undirected graph with $n$ vertices, $m$ edges, and cut-size parameter $k$. In this work, we show the first close-to-linear time parameterized algorithm that computes an unbreakable decomposition. More precisely, for any $0<ε\leq 1$, our algorithm runs in time $2^{O(\frac{k}ε \log \frac{k}ε)}m^{1 + ε}$ and computes a $(O(k/ε), k)$ unbreakable tree decomposition of $G$, where each bag has adhesion at most $O(k/ε)$. This immediately opens up possibilities for obtaining close-to-linear time algorithms for numerous problems whose only known solution is based on unbreakable decomposition.

cs.DS↗

arXiv2024

Approximating Small Sparse Cuts

We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\, k)$-approximation algorithms for various versions in this setting. Our techniques involve an extension of the notion of sample sets (Feige and Mahdian STOC'06), originally developed for small balanced cuts, to sparse cuts in general. We then show how to combine this notion of sample sets with two algorithms, one based on an existing framework of LP rounding and another new algorithm based on the cut-matching game, to get such approximation algorithms. Our cut-matching game algorithm can be viewed as a local version of the cut-matching game by Khandekar, Khot, Orecchia and Vishnoi and certifies an expansion of every vertex set of size $s$ in $\mathcal{O}(\log s)$ rounds. These techniques may be of independent interest. As corollaries of our results, we also obtain an $\mathcal{O}(\log opt)$-approximation for min-max graph partitioning, where $opt$ is the min-max value of the optimal cut, and improve the bound on the size of multicut mimicking networks computable in polynomial time.

cs.DS↗

arXiv2024

Separating $k$-Median from the Supplier Version

Given a metric space $(V, d)$ along with an integer $k$, the $k$-Median problem asks to open $k$ centers $C \subseteq V$ to minimize $\sum_{v \in V} d(v, C)$, where $d(v, C) := \min_{c \in C} d(v, c)$. While the best-known approximation ratio of $2.613$ holds for the more general supplier version where an additional set $F \subseteq V$ is given with the restriction $C \subseteq F$, the best known hardness for these two versions are $1+1/e \approx 1.36$ and $1+2/e \approx 1.73$ respectively, using the same reduction from Max $k$-Coverage. We prove the following two results separating them. First, we show a $1.546$-parameterized approximation algorithm that runs in time $f(k) n^{O(1)}$. Since $1+2/e$ is proved to be the optimal approximation ratio for the supplier version in the parameterized setting, this result separates the original $k$-Median from the supplier version. Next, we prove a $1.416$-hardness for polynomial-time algorithms assuming the Unique Games Conjecture. This is achieved via a new fine-grained hardness of Max-$k$-Coverage for small set sizes. Our upper bound and lower bound are derived from almost the same expression, with the only difference coming from the well-known separation between the powers of LP and SDP on (hypergraph) vertex cover.

cs.DS↗

arXiv2022

A wavelet-based detector function for characterizing intermittent velocity signals

In this work, we propose a new detector function based on wavelet transform to discriminate between turbulent and non-turbulent regions in an intermittent velocity signal. The derivative-based detector function, which is commonly used in intermittency calculation schemes, shows large fluctuations within turbulent parts of the signal and requires averaging over a certain ``smoothing period'' to remove the fake drop-outs, introducing subjectivity in calculating intermittency. The new detector function proposed here is obtained by averaging the ``pre-multiplied wavelet energy'' over the entire frequency range, resulting in a function that is much smoother than the derivative-based detector and at the same time has a good discriminatory property. This makes the choice of the smoothing period unnecessary and removes the subjectivity associated with it. We demonstrate the effectiveness of the wavelet detector within the framework of the widely-used method by Hedley and Keffer (1974, J. Fluid Mech., V64, pp625), for a range of velocity signals representing the different stages of roughness-induced transition. The wavelet detector function works well in detecting the edge intermittency of a canonical turbulent boundary layer as well, thereby highlighting its generality. Our detector can, in principle, be used with any method of specifying threshold for obtaining an indicator function.

physics.flu-dyn↗