Mudassir Shabbir
MS Mudassir Shabbir

Mudassir Shabbir

Associate Professor, Department of Computer Science, LUMS

Graph theory · Discrete geometry · Network science

About

Bio

I am an Associate Professor in the Department of Computer Science at the Lahore University of Management Sciences (LUMS), Pakistan.

I earned my Ph.D. from Rutgers University (2014), where I was a Fulbright Scholar and Rutgers Honors Fellow. Before joining LUMS in 2026 I spent twelve years at the Information Technology University (ITU), Lahore — first as Assistant Professor, then as Associate Professor and Chairperson of the CS Department — and held a concurrent appointment as Research Assistant Professor at Vanderbilt University. I have also worked at Los Alamos National Laboratory and Bloomberg L.P.

My research sits at the intersection of graph machine learning, network science, and discrete geometry. A common thread is using combinatorial and geometric structure — zero forcing, centerpoints, PMI sequences — to reason about resilience, controllability, and representation in networks.

Research

Research Areas

Machine Learning on Graphs

Graph Machine Learning

Graph neural networks for combinatorial optimization (minimum dominating set, minimum vertex cover), code vulnerability detection, and brain connectomics. The NeuroGraph benchmark provides 35 graph datasets spanning behavioral and cognitive traits for reproducible research in neuroimaging.

Distributed Systems · Fault Tolerance

Resilient Multi-Agent Systems

Byzantine-resilient consensus and distributed learning using the centerpoint theorem. Applications include multi-robot pursuit, distributed SGD under adversarial attacks, GNN-based flocking control, and resilient multi-agent reinforcement learning.

Control Theory · Combinatorics

Network Controllability & Robustness

Strong structural controllability via zero forcing sets and distance-based bounds, with algorithms for leader selection and edge augmentation. PMI sequences and their tight bounds connect discrete geometry to network controllability.

PMI Sequences paper PMI algorithm
Computational Geometry · Algorithms

Discrete & Computational Geometry

Centerpoint theorem, ray-shooting depth, and k-centerpoint conjectures in ℝd. Affine-invariant statistical depth measures and their algorithms. PhD thesis: hitting sets in convex ranges from Rutgers (Fulbright, 2014).

Working Papers
Spectral Graph Theory
On the Number of Generalized Cospectral Mates of Graphs
M. Raza · O. U. Ahmad · M. Shabbir · W. Abbas  ·  LUMS & UT Dallas
Upper bound on cospectral multiplicity via the Smith Normal Form of the walk matrix — a quantitative arithmetic criterion extending beyond binary DGS classification.
Under Review Read more →
Discrete Mathematics · Combinatorics
PMI Sequence — An Erdős-Szekeres Type Result
M. Shabbir  ·  LUMS
Tight asymptotic bounds Θ((d!·n)1/d) on the longest pairwise monotone increasing sequence in n-point subsets of ℤ≥0d.
In Preparation Read more →
Spectral Graph Theory · Ring Theory
Cospectral Mates — Ring-Theoretic Extension
M. Raza · O. U. Ahmad · M. Shabbir · W. Abbas
Ring-theoretic view of walk-matrix arithmetic constraints. The elementary divisors of W(G) over ℤ control the multiplicity of generalized cospectral mates.
Working Paper Read more →
Graph Theory · Reconstruction
Reconstructability vs. Godsil-McKay Switching
M. Shabbir  ·  LUMS
Can Godsil-McKay switching produce reconstruction counterexamples? Partial result: degree-altering switchings are always deck-distinguishable.
Working Note Read more →
Notes & questions

Blogs

Explorations of graphs, computation, and the questions they lead to.

All blog entries →

Open Source

Software Projects

Goldex — Coin Extractor

Playable 2D/3D game visualizing the extractor model behind distance-based bounds on strong structural controllability. Move horizontal and vertical extractors across a coin grid — mechanics that directly mirror the combinatorial structure of the research.

React Vite Research Demo Live Game
Speak

Native macOS presentation app. Compose PDFs, videos, and images into a single plan with per-slide hotkeys for branching, live pen/highlighter drawing overlay, and fullscreen HUD. Built entirely on Apple frameworks — no dependencies.

Swift SwiftUI PDFKit AVKit macOS 14+
Lame

macOS app for browsing and deleting photos and videos from USB-connected phones. iPhones via ImageCaptureCore; Android via libmtp with an ADB fallback for Samsung Galaxy devices. Thumbnail grid, bulk deletion, sorting and filtering.

Swift SwiftUI ImageCaptureCore libmtp
PDF Util

Desktop PDF page-management app. Drag-and-drop reordering, extraction, deletion, insertion from another PDF, rotation, and full-resolution page preview. Undo/redo for all operations. Cross-platform via Electron.

TypeScript React Electron pdf-lib dnd-kit
Quiz Game

Live classroom quiz tool: a PDF question bank fills the screen while a sidebar tracks scores for up to five teams against a 90-minute countdown. Correct/Incorrect/Pass buttons and full keyboard shortcuts — no setup, just open and play.

Vanilla JS Electron Live App
Exam Timer

Full-featured countdown timer for exam halls. Preset durations, custom time entry, add-5-minutes button, editable title, light/dark theme, animation controls, fullscreen mode, and state persistence across refreshes.

React JavaScript Live Demo
CrowdFunding DApp

Fully decentralized crowdfunding platform on Ethereum. Community members propose projects, vote, execute approved proposals, and contribute funds — all through auditable smart contracts with a React frontend.

Solidity React Hardhat Ethereum
Set Operations Practice

Flashcard quiz for discrete math students. Each round generates two random sets and asks for the union, intersection, or set difference — with four multiple-choice answers and instant feedback.

React Next.js TypeScript Live App
Teaching

Courses

Algorithms
CS310 / CS5102
Spring 2026 · LUMS

Undergraduate and graduate algorithms: asymptotic analysis, divide-and-conquer, graph algorithms, dynamic programming, NP-completeness, and randomized algorithms. Course website with lecture notes, schedule, and announcements.

Live Course Site
Algorithms
CS310 / CS5102
Spring 2025 · ITU

27 lectures of notes (LaTeX + compiled PDFs) covering MST, BFS/DFS, articulation points, network flow, dynamic programming, string matching, and more. Python implementations of Kruskal's, Prim's, and topological sort.

Lecture Notes + Code
Discrete Math
Discrete Structures
Fall 2026 · LUMS

Course website for Discrete Structures with syllabus, weekly schedule, lecture notes, worksheets, and homework. Data-driven single-page site that updates automatically when JSON files are edited.

Live Course Site
Special Lecture
The Axiom of Choice
Discrete Mathematics · Visual Lecture

A standalone 29-slide visual lecture on ZF, choice functions, independence, well-ordering, Banach–Tarski, non-measurable sets, and when selection rules can replace Choice.

Standalone HTML Visual Slides
Math Circle
GLITCH!
Error-Correcting Codes · Interactive Workshop

A puzzle-led mathematics circle on parity, Hamming distance, Hamming(7,4), Golay, and Reed–Solomon codes, with an interactive slide deck and four printable worksheets.

Interactive Slides Worksheets
Research Internship
RISE Program
Summer 2025 · LUMS

Four-week mathematics research program for A-level students (ages 16–18). Topics: graph theory, zero forcing and network controllability, Erdős–Szekeres, and the centerpoint theorem — active open problems, accessible with no university background.

Interactive Demos Colab Notebooks Handouts
Media

Video Lectures & Animations

I produce animated explainers and lecture recordings on algorithms, discrete mathematics, and theoretical computer science — aimed at undergraduates and anyone curious about the ideas behind the math. Two channels, two flavours:

Idea Behind
@ideabehind5680

Short animated explainers on the core idea behind classic algorithms — median-of-medians, Kruskal's MST, zero forcing, and more. Produced with Manim; designed to build intuition before the formal proof.
Theory Group
@theorygroup780

Longer-form lecture recordings covering discrete structures, graph theory, and algorithms at university level. Companion to classroom teaching at LUMS and ITU.
Research Output

Publications

  • On the Enumeration of Generalized Cospectral Mates of Graphs
    Muhammad Raza, Obaid Ullah Ahmad, Mudassir Shabbir, Waseem Abbas
    arXiv:2601.07373 (2026)
    Establishes tight asymptotic bounds on the number of generalized cospectral mates of graphs via a combinatorial enumeration method based on the Smith Normal Form of the walk matrix — yielding an explicit count for a broad family of graphs.
    Paper
  • Controllability Backbone in Multiagent Networks
    Mudassir Shabbir, Waseem Abbas
    Automatica (2026)
    Identifies a minimal controllability-preserving subgraph — the backbone — in multiagent networks with distributed linear dynamics. Backbone structure is characterized via zero forcing, with polynomial-time algorithms for extraction and edge augmentation.
    Paper
  • Walk Matrix-Based Upper Bounds on Generalized Cospectral Mates
    Muhammad Raza, Mudassir Shabbir, Waseem Abbas
    arXiv:2507.06927 (2025)
    Upper bounds on the number of non-isomorphic generalized cospectral mates derived from arithmetic properties of the walk matrix determinant, applicable to the broad family ℋₙ.
    Paper
  • Learning Backbones: Sparsifying Graphs through Zero Forcing for Effective Graph-Based Learning
    Obaid Ullah Ahmad, Anwar Said, Mudassir Shabbir, Xenofon Koutsoukos, Waseem Abbas
    arXiv:2502.17713 (2025)
    A graph sparsification approach using zero forcing sets to extract learning-effective backbones from dense graphs, improving GNN performance and scalability while preserving structural properties relevant to downstream tasks.
    Paper
  • Feature Construction Using Network Control Theory and Rank Encoding for Graph Machine Learning
    Anwar Said, Yingbo Wei, Obaid Ullah Ahmad, Mudassir Shabbir, Waseem Abbas, Xenofon Koutsoukos
    IEEE Open Journal of Control Systems (2025)
    A network control-theoretic feature construction method using rank encoding of controllability Gramians, producing expressive node features that outperform spectral and positional baselines on multiple benchmarks.
  • Control-based Conditions for Graph Distinguishability
    Muhammad Raza, Obaid Ullah Ahmad, Mudassir Shabbir, Xenofon Koutsoukos, Waseem Abbas
    Proc. Conference on Control and its Applications (CT), SIAM, pp. 31–38 (2025)
    Arithmetic conditions on the walk matrix characterizing when a graph is determined by its generalized spectrum, with applications to the graph distinguishability problem.
  • Resilient Distributed Learning in Multi-UAV Systems
    Nathan Potteiger, Mudassir Shabbir, Scott Eisele, Markus Wutka, Xenofon Koutsoukos
    Smarter Cyber Physical Systems, Springer, pp. 543–567 (2025)
    A Byzantine-resilient distributed learning framework for multi-UAV systems that tolerates adversarial agents using geometric median aggregation, with convergence guarantees under communication attacks.
  • NeuroGraph: Benchmarks for Graph Machine Learning in Brain Connectomics
    Anwar Said, Roza G. Bayrak, Tyler Derr, Mudassir Shabbir, Daniel Moyer, Catie Chang, Xenofon Koutsoukos
    Advances in Neural Information Processing Systems (NeurIPS 2023)
    A benchmark suite of 35 graph-based neuroimaging datasets spanning behavioral and cognitive traits, with 15+ baseline methods and an open-source Python package for graph ML in brain connectomics.
    Paper
  • Sequential Graph Neural Networks for Source Code Vulnerability Identification
    Ammar Ahmed, Anwar Said, Mudassir Shabbir, Xenofon Koutsoukos
    Neural Computing and Applications (2023)
    SEGNN — a sequential GNN achieving state-of-the-art vulnerability identification by learning code semantic representations via graph convolution, trained on the curated CVEFGE dataset.
    Paper
  • Conversations in the Wild: Data Collection, Automatic Generation and Evaluation
    Nimra Zaheer, Agha Ali Raza, Mudassir Shabbir
    Computer Speech & Language 89, 101699 (2024)
    Data collection, automatic generation, and evaluation methodology for conversational datasets in naturalistic settings, with benchmarks on coherence, diversity, and human evaluation alignment.

Full list on Google Scholar.

Curriculum Vitae

Experience

Full CV (PDF)
  • 2026 – present
    LUMS
    Associate Professor
    Department of Computer Science
  • 2021 – 2023
    Vanderbilt University
    Research Assistant Professor
  • 2014 – 2026
    Information Technology University
    Assistant / Associate Professor
    Theory Group · Chairperson, Department of Computer Science (2021–2025)
  • 2013
    Bloomberg L.P.
    Research Intern
    New York, NY
  • 2011
    Los Alamos National Laboratory
    Research Intern
    Los Alamos, NM
  • 2010 – 2014
    Rutgers University
    Ph.D. Student
    Division of Computer Science · Fulbright Scholarship · Rutgers Honors Fellow 2011–12
  • Summer 2010
    LUMS
    Research Assistant
    Discrete & Computational Geometry · hosted by Prof. Nabil Mustafa
  • 2008 – 2010
    Rutgers University
    M.S. Student
    Division of Computer Science · Fulbright Scholarship