Related papers: A brief note on approximate optimization of submod…
This work provides performance guarantees for the greedy solution of experimental design problems. In particular, it focuses on A- and E-optimal designs, for which typical guarantees do not apply since the mean-square error and the maximum…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Submodular maximization with a cardinality constraint can model various problems, and those problems are often very large in practice. For the case where objective functions are monotone, many fast approximation algorithms have been…
Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we…
This paper presents a polynomial-time $1/2$-approximation algorithm for maximizing nonnegative $k$-submodular functions. This improves upon the previous $\max\{1/3, 1/(1+a)\}$-approximation by Ward and \v{Z}ivn\'y~(SODA'14), where…
Maximization of {\it non-submodular} functions appears in various scenarios, and many previous works studied it based on some measures that quantify the closeness to being submodular. On the other hand, many practical non-submodular…
Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…
Submodular optimization plays a key role in many real-world problems. In many real-world scenarios, it is also necessary to handle uncertainty, and potentially disruptive events that violate constraints in stochastic settings need to be…
We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a nondecreasing submodular…
We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove…
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…
We study a linear quadratic regulation problem with a constraint where the control input can be nonzero only at a limited number of times. Given that this constraint leads to a combinational optimization problem, we adopt a greedy method to…
A $k$-submodular function is an extension of a submodular function in that its input is given by $k$ disjoint subsets instead of a single subset. For unconstrained nonnegative $k$-submodular maximization, Ward and \v{Z}ivn\'y proposed a…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
The problem of minimization of a quadratic functional depending on great number of binary variables is examined. 3 variants of minimization procedure are studied with the aid of computer simulation for spin-glass matrices. It is shown that…
We study the problem of distributed state estimation in a network of sensing units that can exchange their measurements but the rate of communication between the units is constrained. The units collect noisy, possibly only partial…
Collective communications are ubiquitous in parallel applications. We present two new algorithms for performing a reduction. The operation associated with our reduction needs to be associative and commutative. The two algorithms are…
We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained…
We present new tight performance guarantees for the greedy maximization of nondecreasing submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a…
Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and…