Related papers: Combinatorics of the change-making problem
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
We study minimum entropy submodular optimization, a common generalization of the minimum entropy set cover problem, studied earlier by Cardinal et al., and the submodular set cover problem. We give a general bound of the approximation…
The method of alternating projections involves projecting an element of a Hilbert space cyclically onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm and that one can obtain estimates for…
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…
The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy…
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…
This paper studies the problem of modifying the input matrix of a structured system to make the system strongly structurally controllable. We focus on the generalized structured systems that rely on zero/nonzero/arbitrary structure, i.e.,…
We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimality of the coin-betting formulation among e-variable-based…
We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists,…
We study mechanisms that use greedy allocation rules and pay-your-bid pricing to allocate resources subject to a matroid constraint. We show that all such mechanisms obtain a constant fraction of the optimal welfare at any equilibrium of…
In this work, we study the multi-agent decision problem where agents try to coordinate to optimize a given system-level objective. While solving for the global optimal is intractable in many cases, the greedy algorithm is a well-studied and…
The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…
We consider auctions in which greedy algorithms, paired with first-price or critical-price payment rules, are used to resolve multi-parameter combinatorial allocation problems. We study the price of anarchy for social welfare in such…
The greedy algorithm A iterates over a set of uniformly sized independent sets of a given graph G and checks for each set S which non-neighbor of S, if any, is best suited to be added to S, until no more suitable non-neighbors are found for…
We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein…
In the Shortest Common Superstring problem (SCS), one needs to find the shortest superstring for a set of strings. While SCS is NP-hard and MAX-SNP-hard, the Greedy Algorithm "choose two strings with the largest overlap; merge them; repeat"…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
We use Markov chains and numerical linear algebra -- and several CPU hours -- to determine the expected number of coins in a person's possession under certain conditions. We identify the spending strategy that results in the minimum…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…