arXiv subjects

Sanjukta Roy

Publications and source records attributed to Sanjukta Roy.

35 records · Page 2Linked to original sources

arXiv2023

Maximizing Social Welfare in Score-Based Social Distance Games

Social distance games have been extensively studied as a coalition formation model where the utilities of agents in each coalition were captured using a utility function u that took into account distances in a given social network. In this paper, we consider a non-normalized score-based definition of social distance games where the utility function u_v depends on a generic scoring vector v, which may be customized to match the specifics of each individual application scenario. As our main technical contribution, we establish the tractability of computing a welfare-maximizing partitioning of the agents into coalitions on tree-like networks, for every score-based function u_v. We provide more efficient algorithms when dealing with specific choices of u_v or simpler networks, and also extend all of these results to computing coalitions that are Nash stable or individually rational. We view these results as a further strong indication of the usefulness of the proposed score-based utility function: even on very simple networks, the problem of computing a welfare-maximizing partitioning into coalitions remains open for the originally considered canonical function u.

cs.GT↗

arXiv2023

Optimal Seat Arrangement: What Are the Hard and Easy Cases?

We study four NP-hard optimal seat arrangement problems [Bodlaender et al., 2020a], which each have as input a set of n agents, where each agent has cardinal preferences over other agents, and an n-vertex undirected graph (called seat graph). The task is to assign each agent to a distinct vertex in the seat graph such that either the sum of utilities or the minimum utility is maximized, or it is envy-free or exchange-stable. Aiming at identifying hard and easy cases, we extensively study the algorithmic complexity of the four problems by looking into natural graph classes for the seat graph (e.g., paths, cycles, stars, or matchings), problem-specific parameters (e.g., the number of non-isolated vertices in the seat graph or the maximum number of agents towards whom an agent has non-zero preferences), and preference structures (e.g., non-negative or symmetric preferences). For strict preferences and seat graphs with disjoint edges and isolated vertices, we correct an error by Bodlaender et al. [2020b] and show that finding an envy-free arrangement remains NP-hard in this case.

cs.GT↗

arXiv2023

Hedonic Games With Friends, Enemies, and Neutrals: Resolving Open Questions and Fine-Grained Complexity

We investigate verification and existence problems for prominent stability concepts in hedonic games with friends, enemies, and optionally with neutrals [8, 16]. We resolve several (long-standing) open questions [4, 16, 20, 23] and show that for friend-oriented preferences, under the friends and enemies model, it is coNP-complete to verify whether a given agent partition is (strictly) core stable, while under the friends, enemies, and neutrals model, it is NP-complete to determine whether an individual stable partition exists. We further look into natural restricted cases from the literature, such as when the friends and enemies relationships are symmetric, when the initial coalitions have bounded size, when the vertex degree in the friendship graph (resp. the union of friendship and enemy graph) is bounded, or when such graph is acyclic or close to being acyclic. We obtain a complete (parameterized) complexity picture regarding these cases.

cs.GT↗

arXiv2022

Degreewidth: a New Parameter for Solving Problems on Tournaments

In the paper, we define a new parameter for tournaments called degreewidth which can be seen as a measure of how far is the tournament from being acyclic. The degreewidth of a tournament $T$ denoted by $Δ(T)$ is the minimum value $k$ for which we can find an ordering $\langle v_1, \dots, v_n \rangle$ of the vertices of $T$ such that every vertex is incident to at most $k$ backward arcs (\textit{i.e.} an arc $(v_i,v_j)$ such that $j<i$). Thus, a tournament is acyclic if and only if its degreewidth is zero. Additionally, the class of sparse tournaments defined by Bessy et al. [ESA 2017] is exactly the class of tournaments with degreewidth one. We first study computational complexity of finding degreewidth. Namely, we show it is NP-hard and complement this result with a $3$-approximation algorithm. We also provide a cubic algorithm to decide if a tournament is sparse. Finally, we study classical graph problems \textsc{Dominating Set} and \textsc{Feedback Vertex Set} parameterized by degreewidth. We show the former is fixed parameter tractable whereas the latter is NP-hard on sparse tournaments. Additionally, we study \textsc{Feedback Arc Set} on sparse tournaments.

cs.DM↗

arXiv2022

Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space

We investigate the Euclidean $d$-Dimensional Stable Roommates problem, which asks whether a given set~$V$ of $d \cdot n$ points from the 2-dimensional Euclidean space can be partitioned into $n$ disjoint (unordered) subsets $Π=\{V_1,\ldots,V_{n}\}$ with $|V_i|=d$ for each $V_i\in Π$ such that $Π$ is stable. Here, stability means that no point subset $W\subseteq V$ is blocking $Π$ and $W$ is said to be blocking $Π$ if $|W|= d$ such that $\sum_{w'\in W}δ(w,w') < \sum_{v\in Π(w)}δ(w,v)$ holds for each point $w\in W$, where $Π(w)$ denotes the subset $V_i\in Π$ which contains $w$ and $δ(a,b)$ denotes the Euclidean distance between points $a$ and $b$. Complementing the existing known polynomial-time result for $d=2$, we show that such polynomial-time algorithms cannot exist for any fixed number $d \ge 3$ unless P=NP. Our result for $d=3$ answers a decade-long open question in the theory of Stable Matching and Hedonic Games [17, 1, 9, 25, 20].

cs.GT↗

arXiv2022

Transition frequency measurement of highly excited Rydberg states of 87Rb for a wide range of principal quantum numbers

We report our measurements of the absolute transition frequencies of 5P_3/2,F = 3 to nS and nD Rydberg states of 87Rb with high principal quantum numbers in a wide range of values (n = 45-124). The measurements were performed using Rydberg Electromagnetically Induced Transparency (EIT) in ladder-type three-level systems. We measure the transition frequencies with an accuracy of less than 2 MHz. We determine the values of the Rydberg-Ritz parameter for 87Rb from our experimental measurements of the transition frequencies. Our measurements of the absolute transition frequencies of the highly excited Rydberg states would be useful for diverse applications in quantum information processing, quantum simulation and quantum sensing with Rydberg atoms.

physics.atom-ph↗

arXiv2022

Parameterized Intractability for Multi-Winner Election under the Chamberlin-Courant Rule and the Monroe Rule

Answering an open question by Betzler et al. [Betzler et al., JAIR'13], we resolve the parameterized complexity of the multi-winner determination problem under two famous representation voting rules: the Chamberlin-Courant (in short CC) rule [Chamberlin and Courant, APSR'83] and the Monroe rule [Monroe, APSR'95]. We show that under both rules, the problem is W[1]-hard with respect to the sum $β$ of misrepresentations, thereby precluding the existence of any $f(β) \cdot |I|^{O(1)}$ -time algorithm, where $|I|$ denotes the size of the input instance.

cs.MA↗

arXiv2021

Measurements and analysis of response function of cold atoms in optical molasses

We report our experimental measurements and theoretical analysis of the position response function of a cloud of cold atoms residing in the viscous medium of an optical molasses and confined by a magneto-optical trap (MOT). We measure the position response function by applying a transient homogeneous magnetic field as a perturbing force. We observe a transition from a damped oscillatory motion to an over-damped relaxation, stemming from a competition between the viscous drag provided by the optical molasses and the restoring force of the MOT. Our observations are in both qualitative and quantitative agreement with the predictions of a theoretical model based on the Langevin equation. As a consistency check, and as a prototype for future experiments, we also study the free diffusive spreading of the atomic cloud in our optical molasses with the confining magnetic field of the MOT turned off. We find that the measured value of the diffusion coefficient agrees with the value predicted by our Langevin model, using the damping coefficient. The damping coefficient was deduced from our measurements of the position response function at the same temperature.

physics.atom-ph↗

arXiv2021

Gerrymandering on graphs: Computational complexity and parameterized algorithms

Partitioning a region into districts to favor a particular candidate or a party is commonly known as gerrymandering. In this paper, we investigate the gerrymandering problem in graph theoretic setting as proposed by Cohen-Zemach et al. [AAMAS 2018]. Our contributions in this article are two-fold, conceptual and computational. We first resolve the open question posed by Ito et al. [AAMAS 2019] about the computational complexity of the problem when the input graph is a path. Next, we propose a generalization of their model, where the input consists of a graph on $n$ vertices representing the set of voters, a set of $m$ candidates $\mathcal{C}$, a weight function $w_v: \mathcal{C}\rightarrow {\mathbb Z}^+$ for each voter $v\in V(G)$ representing the preference of the voter over the candidates, a distinguished candidate $p\in \mathcal{C}$, and a positive integer $k$. The objective is to decide if one can partition the vertex set into $k$ pairwise disjoint connected sets (districts) s.t $p$ wins more districts than any other candidate. The problem is known to be NPC even if $k=2$, $m=2$, and $G$ is either a complete bipartite graph (in fact $K_{2,n}$) or a complete graph. This means that in search for FPT algorithms we need to either focus on the parameter $n$, or subclasses of forest. Circumventing these intractable results, we give a deterministic and a randomized algorithms for the problem on paths running in times $2.619^{k}(n+m)^{O(1)}$ and $2^{k}(n+m)^{O(1)}$, respectively. Additionally, we prove that the problem on general graphs is solvable in time $2^n (n+m)^{O(1)}$. Our algorithmic results use sophisticated technical tools such as representative set family and Fast Fourier transform based polynomial multiplication, and their (possibly first) application to problems arising in social choice theory and/or game theory may be of independent interest to the community.

cs.DS↗

arXiv2021

Detection of Spin Coherence in Cold Atoms via Faraday Rotation Fluctuations

We report non-invasive detection of spin coherence in a collection of Raman-driven cold atoms using dispersive Faraday rotation fluctuation measurements, which opens up new possibilities of probing spin correlations in quantum gases and other similar systems. We demonstrate five orders of magnitude enhancement of the measured signal strength than the traditional spin noise spectroscopy with thermal atoms in equilibrium. Our observations are in good agreement with the comprehensive theoretical modeling of the driven atoms at various temperatures. The extracted spin relaxation rate of cold rubidium atoms with atom number density $\sim$10$^9/$cm$^3$ is of the order of 2$π\times$0.5 kHz at 150 $μ$K, two orders of magnitude less than $\sim$ 2$π\times$50 kHz of a thermal atomic vapor with atom number density $\sim$10$^{12}/$cm$^3$ at 373 K.

cond-mat.quant-gas↗

arXiv2020

Fractional Matchings under Preferences: Stability and Optimality

We thoroughly study a generalized version of the classic Stable Marriage and Stable Roommates problems where agents may share partners. We consider two prominent stability concepts: ordinal stability [Aharoni and Fleiner, Journal of Combinatorial Theory, 2003] and cardinal stability [Caragiannis et al., ACM EC 2019] and two optimality criteria: maximizing social welfare (i.e., the overall satisfaction of the agents) and maximizing the number of fully matched agents (i.e., agents whose shares sum up to one). After having observed that ordinal stability always exists and implies cardinal stability, and that the set of ordinally stable matchings in a restricted case admits a lattice structure, we obtain a complete picture regarding the computational complexity of finding an optimal ordinally stable or cardinally stable matching. In the process we answer an open question raised by Caragiannis et al. [AIJ 2020].

cs.GT↗

arXiv2020

On the (Parameterized) Complexity of Almost Stable Marriage

In the Stable Marriage problem. when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most real-life situations, where agents participate in the matching market voluntarily and submit their preferences, it is natural to assume that each agent wants to be matched to someone in his/her preference list as opposed to being unmatched. In light of the Rural Hospital Theorem, we have to relax the "no blocking pair" condition for stable matchings in order to match more agents. In this paper, we study the question of matching more agents with fewest possible blocking edges. In particular, we find a matching whose size exceeds that of stable matching in the graph by at least t and has at most k blocking edges. We study this question in the realm of parameterized complexity with respect to several natural parameters, k,t,d, where d is the maximum length of a preference list. Unfortunately, the problem remains intractable even for the combined parameter k+t+d. Thus, we extend our study to the local search variant of this problem, in which we search for a matching that not only fulfills each of the above conditions but is "closest", in terms of its symmetric difference to the given stable matching, and obtain an FPT algorithm.

cs.GT↗

arXiv2018

Measurements of spin properties of atomic systems in and out of equilibrium via noise spectroscopy

We explore the applications of spin noise spectroscopy (SNS) for detection of the spin properties of atomic ensembles in and out of equilibrium. In SNS, a linearly polarized far-detuned probe beam on passing through an ensemble of atomic spins acquires the information of the spin correlations of the system which is extracted using its time-resolved Faraday-rotation noise. We measure various atomic, magnetic and sub-atomic properties as well as perform precision magnetometry using SNS in rubidium atomic vapor in thermal equilibrium. Thereafter, we manipulate the relative spin populations between different ground state hyperfine levels of rubidium by controlled optical pumping which drives the system out of equilibrium. We then apply SNS to probe such spin imbalance nonperturbatively. We further use this driven atomic vapor to demonstrate that SNS can have better resolution than typical absorption spectroscopy in detecting spectral lines in the presence of various spectral broadening mechanisms.

physics.atom-ph↗

arXiv2017

Balanced Stable Marriage: How Close is Close Enough?

The Balanced Stable Marriage problem is a central optimization version of the classic Stable Marriage problem. Here, the output cannot be an arbitrary stable matching, but one that balances between the dissatisfaction of the two parties, men and women. We study Balanced Stable Marriage from the viewpoint of Parameterized Complexity. Our "above guarantee parameterizations" are arguably the most natural parameterizations of the problem at hand. Indeed, our parameterizations precisely fit the scenario where there exists a stable marriage that both parties would accept, that is, where the satisfaction of each party is "close" to the best it can hope for. Furthermore, our parameterizations accurately draw the line between tractability and intractability with respect to the target value.

cs.DS↗

arXiv2014

Measurement of the mobility edge for 3D Anderson localization

Anderson localization is a universal phenomenon affecting non-interacting quantum particles in disorder. In three spatial dimensions it becomes particularly interesting to study because of the presence of a quantum phase transition from localized to extended states, predicted by P.W. Anderson in his seminal work, taking place at a critical energy, the so-called mobility edge. The possible relation of the Anderson transition to the metal-insulator transitions observed in materials has originated a flurry of theoretical studies during the past 50 years, and it is now possible to predict very accurately the mobility edge starting from models of the microscopic disorder. However, the experiments performed so far with photons, ultrasound and ultracold atoms, while giving evidence of the transition, could not provide a precise measurement of the mobility edge. In this work we are able to obtain such a measurement using an ultracold atomic system in a disordered speckle potential, thanks to a precise control of the system energy. We find that the mobility edge is close to the mean disorder energy at small disorder strengths, while a clear effect of the spatial correlation of the disorder appears at larger strengths. The precise knowledge of the disorder properties in our system offers now the opportunity for an unprecedented experiment-theory comparison for 3D Anderson localization, which is also a necessary step to start the exploration of novel regimes for many-body disordered systems.

cond-mat.dis-nn↗

arXiv2013

Universality of the three-body Efimov parameter at narrow Feshbach resonances

We measure the critical scattering length for the appearance of the first three-body bound state, or Efimov three-body parameter, at seven different Feshbach resonances in ultracold 39K atoms. We study both intermediate and narrow resonances, where the three-body spectrum is expected to be determined by the non-universal coupling of two scattering channels. We observe instead approximately the same universal relation of the three-body parameter with the two-body van der Waals radius already found for broader resonances, which can be modeled with a single channel. This unexpected observation suggests the presence of a new regime for three-body scattering at narrow resonances.

cond-mat.quant-gas↗

arXiv2012

Direct evaporative cooling of 39K atoms to Bose-Einstein condensation

We report the realization of Bose-Einstein condensates of 39K atoms without the aid of an additional atomic coolant. Our route to Bose-Einstein condensation comprises Sub Doppler laser cooling of large atomic clouds with more than 10^10 atoms and evaporative cooling in optical dipole traps where the collisional cross section can be increased using magnetic Feshbach resonances. Large condensates with almost 10^6 atoms can be produced in less than 15 seconds. Our achievements eliminate the need for sympathetic cooling with Rb atoms which was the usual route implemented till date due to the unfavourable collisional property of 39K. Our findings simplify the experimental set-up for producing Bose-Einstein condensates of 39K atoms with tunable interactions, which have a wide variety of promising applications including atom-interferometry to studies on the interplay of disorder and interactions in quantum gases.

cond-mat.quant-gas↗