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In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear…
To tackle the exponentiality associated with NP-hard problems, two paradigms have been proposed. First, Branch & Bound, like Dynamic Programming, achieve efficient exact inference but requires extensive information and analysis about the…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…
Many algorithms for maximizing a monotone submodular function subject to a knapsack constraint rely on the natural greedy heuristic. We present a novel refined analysis of this greedy heuristic which enables us to: $(1)$ reduce the…
In this paper we present a collection of results pertaining to haplotyping. The first set of results concerns the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype data. More…
Patient cohort retrieval is a pivotal task in medical research and clinical practice, enabling the identification of specific patient groups from extensive electronic health records (EHRs). In this work, we address the challenge of cohort…
The Fibonacci heap is a classic data structure that supports deletions in logarithmic amortized time and all other heap operations in O(1) amortized time. We explore the design space of this data structure. We propose a version with the…
Numerical algorithms for elliptic partial differential equations frequently employ error estimators and adaptive mesh refinement strategies in order to reduce the computational cost. We can extend these techniques to general vectors by…
Transferrable neural architecture search can be viewed as a binary optimization problem where a single optimal path should be selected among candidate paths in each edge within the repeated cell block of the directed a cyclic graph form.…
An algorithm is presented that efficiently solves the selection problem: finding the k-th smallest member of a set. Relevant to a divide-and-conquer strategy, the algorithm also partitions a set into small and large valued subsets. Applied…
We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such…
Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…
This paper addresses the problem of optimal control using search trees. We start by considering multi-armed bandit problems with continuous action spaces and propose LD-HOO, a limited depth variant of the hierarchical optimistic…
This article considers the parallel machine scheduling problem with step-deteriorating jobs and sequence-dependent setup times. The objective is to minimize the total tardiness by determining the allocation and sequence of jobs on identical…
Heuristic algorithms such as simulated annealing, Concorde, and METIS are effective and widely used approaches to find solutions to combinatorial optimization problems. However, they are limited by the high sample complexity required to…
The selection of hyper-parameters is critical in Deep Learning. Because of the long training time of complex models and the availability of compute resources in the cloud, "one-shot" optimization schemes - where the sets of hyper-parameters…
In this paper, we obtain a number of new simple pseudo-polynomial time algorithms on the well-known knapsack problem, focusing on the running time dependency on the number of items $n$, the maximum item weight $w_\mathrm{max}$, and the…
We propose a novel model for learned query optimization which provides query hints leading to better execution plans. The model addresses the three key challenges in learned hint-based query optimization: reliable hint recommendation…
We propose Deep Hierarchical Machine (DHM), a model inspired from the divide-and-conquer strategy while emphasizing representation learning ability and flexibility. A stochastic routing framework as used by recent deep neural…
Hypertree decompositions of hypergraphs are a generalization of tree decompositions of graphs. The corresponding hypertree-width is a measure for the cyclicity and therefore tractability of the encoded computation problem. Many NP-hard…