# Debmalya panigrahi

### Professor

### Department of Computer Science

### Duke University

## NEWS

September '22: Neurips 2022 papers

Online Algorithms with ε-Accurate Predictions: We give online algorithms that are substantially better than worst-case even when given a very weak ML predictor, say one that gives good advice only 1% of the time.

Online Algorithms for the Santa Claus Problem: We give algorithms to allocate a set of items that arrive over time among agents that value them differently in a way that seeks to maximize the minimum cumulative value derived by any agent from the allocation.

June '22: FOCS 2022 paper

All-pairs min-cuts (Gomory-Hu tree) in Õ(n

^{2}) time (breaks Gomory and Hu's 60-year-old bound for the problem!)

May '22: ICML 2022 paper

Online Algorithms with Multiple Predictions: If a diverse set of ML models (and human experts) give different suggestions to a learning-augmented online algorithm, how should the algorithm choose the best advice? We answer this question for a wide range of online optimization problems that can be formulated as covering problems (and some further extensions).

February '22: STOC 2022 paper

Connectivity Augmentation and Splitting Off: We bypass the maxflow bottleneck from our SODA 22 paper by designing a new algorithm for finding the extreme sets using a series of reductions that go all the way from finding arbitrary extreme sets to those that 2-respect a path. These reductions also apply to the minimum cut problem and offer an (arguably simpler) alternative for Karger's near-linear time mincut algorithm.

December '21: SIGMOD 2022 paper

Learning Selectivity Functions (with applications to query processing): We show that selectivity queries that are represented by range spaces with finite VC dimension can be PAC-learned by deriving a bound on the fat shattering dimension of the selectivity functions.

December '21: AAAI 2022 paper

Learning Influence Adoption in Heterogeneous Networks: We give a PAC-learning framework for understanding how a label (e.g., whether a person is infected by a transmissible disease) propagates through a network where each individual node reacts differently to exposure (e.g., depending on their age, co-morbidities, etc.)

October '21: SODA 2022 papers

Connectivity Augmentation and Splitting-Off: We give new algorithms for the edge connectivity augmentation and edge splitting-off problems using the isolating cuts framework that we introduced in a FOCS 2020 paper. This is the first improvement for these problems since the work of Benczur and Karger in 2000.

Online Graph Algorithms with ML Predictions: We give an algorithmic framework for network design problems like Steiner tree, Steiner forest, and facility location in the online algorithms with predictions model. One of the main contributions is a new model for measuring the error of a prediction for metric/graph problems that takes into account both the possibility of inaccurate predictions and complete mispredictions.

September '21: Neurips 2021 paper

Regression for Learning-Augmented Online Algorithms: We bring a regression approach to the area of learning-augmented online algorithms. Our mian contribution is a regression framework and the design of a new loss function that helps make predictions using a PAC learning model for a broad class of online algorithms.

August '21: FOCS 2021 papers

Minimum Cut in Directed Graphs: We give an algorithm to find a minimum cut in a

*directed graph*using (roughly) \tilde{O}(\sqrt{*m*}) max-flow calls. This is the first improvement for the problem since the work of Hao and Orlin in 1992.All-Pairs Minimum Cuts: We give an algorithm that finds the edge connectivity between all pairs of vertices in \tilde{O}(

*n*^2) time for simple graphs. This is optimal if the edge connectivity of every pair is represented explicitly.Online Algorithm for

*k*-Server and Extensions: We give an algorithm for the*k*-server problem and its extension to time windows that has a poly-logarithmic competitive ratio. Our main technical contribution is a new "hitting set" LP formulation of the*k*-server problem that could be useful in resolving the randomized*k*-server conjecture. (Our competitive ratio currently depends on the size and aspect ratio of the metric space in addition to the number of servers*k*.)

February '21: STOC 2021 papers

Approximate Gomory-Hu trees: We give an algorithm that uses only polylog(

*n*) maxflow calls instead of*n*-1 and finds the edge connectivity between all pairs of vertices*up to an arbitrarily small constant approximation*. Previously, the best known was*n-1*max-flows to find*exact*all-pairs connectivities from the work of Gomory and Hu in 1961.Vertex connectivity: We give an algorithm for computing the vertex connectivity of a graph by running polylog(

*n*) maxflow algorithms. This is the first improvement in the running time of the vertex connectivity problem since the work of Henzinger, Rao, and Gabow in 1996.

## about me

I am a Professor of Computer Science at Duke University. Before coming to Duke in 2013, I spent one year as a postdoctoral researcher in the theory group at Microsoft Research Redmond, where I did research in algorithms. In 2012, I obtained my PhD in theoretical computer science at MIT under the supervision of Prof. David Karger by defending this. Before coming to MIT, I worked at Bell Labs in Bangalore for a year, where I did research on algorithms and networks. I obtained my bachelor's and master's degrees in Computer Science and Engineering at Jadavpur University, Kolkata in 2004 and IISc, Bangalore in 2006 respectively. At IISc, I did research in algorithms under the supervision of Prof. Ramesh Hariharan. A long time ago, I grew up in the industrial town of Durgapur where I went to St. Xavier's School.

My CV is available here.

## Research

### Research Interests

I am broadly interested in *theoretical computer science*, particularly in the *design and analysis of algorithms*. My two main research thrusts are **graph algorithms** and **algorithms under uncertainty**. In graph algorithms, I am interested in the study of network flows, graph cuts, and connectivity. Some recent highlights include the fastest deterministic algorithm to find a minimum cut of an undirected graph, the fastest (randomized) algorithms for finding a minimum vertex cut and a minimum cut of a directed graph, and the fastest algorithm for finding the connectivity of all pairs of vertices in an undirected graph. In algorithms under uncertainty, I am interested in both classical online algorithms, and also the design of algorithms that leverage machine learning to overcome worst-case performance barriers. Some recent highlights include new LP relaxations and algorithms for $k$-server and caching problems, and learning-augmented algorithms for fundamental online problems such as weighted caching and ski rental. I also work in approximation algorithms, combinatorial optimization, and algorithmic game theory.

In addition to theoretical research, I am also interested in the design of **algorithms for practical problems**. This includes algorithms for online search, advertising, social networks, and e-commerce, the design and management of computer networks, database management and query processing algorithms, and algorithms with applications in artificial intelligence. I have collaborated with researchers in these areas to design algorithms that are practical, implementable, and scalable. Most of this work has been published in peer-reviewed venues in the application areas, and some of it has led to patents and deployment in prototypes or products.

For a sample of my current research directions, see here.

I am part of the theory group and am also affiliated/collaborate with the CS-econ, AI/ML, and database groups at Duke.

### Publications

A complete list of my publications (along with download links to papers) is available here (arranged chronologically) and here (arranged by topic). You can also download my PhD thesis here.

## Research group

### Openings

I currently have openings for graduate students and undergraduates. I also occasionally have opening for postdocs. Please see here for details.

### Current Students

Keerti Anand (5th year PhD student, jointly advised with Prof. Rong Ge)

Ruoxu Cen (2nd year PhD student)

William He (undergraduate student)

Kevin Sun (5th year PhD student)

Lu Wang (1st year PhD student)

I also often work with Hanrui Zhang.

To see the list of former students and postdocs, please click here.

### Funding

My research has been funded by the National Science Foundation, the Army Research Office, Google, Yahoo!, the Indo-US Science and Technology Forum, and Duke University. I gratefully acknowledge their support.

For more information about my funding, including current grants, please click here.

## teaching

### Current Course

Spring 2023. COMPSCI 638 Graph Algorithms

For a complete list of the courses that I have taught (including links to course material), please click here.

## Contact Information

### Mailing Address

Duke University, Campus Box 90129

308 Research Drive (LSRC Building), Room D203

Durham, NC 27708 USA

Tel: +1 (919) 660-6545

Fax: +1 (919) 660-6519

### E-Mail

The fastest and preferred way to reach me is by email. My username is my first name and the domain is cs.duke.edu