Related papers: End of Potential Line
This thesis addresses the complexities of compiler optimizations, such as register allocation and Lifetime-optimal Speculative Partial Redundancy Elimination (LOSPRE), which are often handled using tree decomposition algorithms. However,…
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
We continue the investigation of parameterized extensions of Linear Temporal Logic (LTL) that retain the attractive algorithmic properties of LTL: a polynomial space model checking algorithm and a doubly-exponential time algorithm for…
A continuous constraint satisfaction problem (CCSP) is a constraint satisfaction problem (CSP) with an interval domain $U \subset \mathbb{R}$. We engage in a systematic study to classify CCSPs that are complete of the Existential Theory of…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
We establish a bound of $O(n^2k^{1+\eps})$, for any $\eps>0$, on the combinatorial complexity of the set $\T$ of line transversals of a collection $\P$ of $k$ convex polyhedra in $\reals^3$ with a total of $n$ facets, and present a…
This paper introduces a computationally efficient method that converges globally to B-stationary points of mathematical programs with equilibrium constraints (MPECs). B-stationarity is necessary for optimality and means that no feasible…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
Orthogonality constraints are ubiquitous in robust and probabilistic machine learning. Unfortunately, current optimizers are computationally expensive and do not scale to problems with hundreds or thousands of constraints. One notable…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
We consider the dynamic resource allocation problem where the decision space is finite-dimensional, yet the solution must satisfy a large or even infinite number of constraints revealed via streaming data or oracle feedback. We model this…
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…
The ever-increasing integration of stochastic renewable energy sources into power systems operation is making the supply-demand balance more challenging. While joint chance-constrained methods are equipped to model these complexities and…
In this paper, I consider a fine-grained dichotomy of Boolean counting constraint satisfaction problem (#CSP), under the exponential time hypothesis of counting version (#ETH). Suppose $\mathscr{F}$ is a finite set of algebraic…
In this paper, we introduce the proper latent decomposition (PLD) as a generalization of the proper orthogonal decomposition (POD) on manifolds. PLD is a nonlinear reduced-order modeling technique for compressing high-dimensional data into…
We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) recently introduced by Emek et al, (STOC 2016). This problem is defined on an underlying $n$-point metric space. An adversary presents real-time requests online…
The last year has witnessed the rapid progress of large language models (LLMs) across diverse domains. Among them, CodeLLMs have garnered particular attention because they can not only assist in completing various programming tasks but also…
We propose an anytime online algorithm for the problem of learning a sequence of adversarial convex cost functions while approximately satisfying another sequence of adversarial online convex constraints. A sequential algorithm is called…
In this paper we propose the PCP-like theorem for sub-linear time inapproximability. Abboud et al. have devised the distributed PCP framework for proving sub-quadratic time inapproximability. Here we try to go further in this direction.…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…