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Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
This paper investigated the problem of embedding a simple Hamiltonian Cycle with n vertices on n points inside a simple polygon. This problem seeks to embed a straight-line cycle (without bends), which does not intersect either itself or…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…
Counting homomorphisms of a constant sized pattern graph $H$ in an input graph $G$ is a fundamental computational problem. There is a rich history of studying the complexity of this problem, under various constraints on the input $G$ and…
We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that…
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…
We show that for each single crossing graph $H$, a polynomially bounded weight function for all $H$-minor free graphs $G$ can be constructed in Logspace such that it gives nonzero weights to all the cycles in $G$. This class of graphs…
This paper considers a recoverable robust single-machine scheduling problem under polyhedral uncertainty with the objective of minimising the total flow time. In this setting, a decision-maker must determine a first-stage schedule subject…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
We solve some computational problems for triangulated closed three-dimensional manifolds using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms for computing the intersection numbers of 1- and 2-dimensional…
The problem of finding the longest simple cycle in a directed graph is NP-hard, with critical applications in computational biology, scheduling, and network analysis. Existing approaches include exact algorithms with exponential runtimes,…
It is a notorious open question whether integer programs (IPs), with an integer coefficient matrix $M$ whose subdeterminants are all bounded by a constant $\Delta$ in absolute value, can be solved in polynomial time. We answer this question…
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…
Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the…
The multilinear framework has achieved the breakthrough $1-1/e$ approximation for maximizing a monotone submodular function subject to a matroid constraint. This framework has a continuous optimization part and a rounding part. We extend…
In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…