Related papers: On the Complexity and Approximation of the Maximum…
We study the approximability of the NP-complete \textsc{Maximum Minimal Feedback Vertex Set} problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type:…
Knapsack problem (KP) is a representative combinatorial optimization problem that aims to maximize the total profit by selecting a subset of items under given constraints on the total weights. In this study, we analyze a generalized version…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
We study the problem of allocating indivisible items on a path among agents. The objective is to find a fair and efficient allocation in which each agent's bundle forms a contiguous block on the line. We say that an instance is \emph{$(a,…
Diversity maximization aims to select a diverse and representative subset of items from a large dataset. It is a fundamental optimization task that finds applications in data summarization, feature selection, web search, recommender…
In machine learning and big data, the optimization objectives based on set-cover, entropy, diversity, influence, feature selection, etc. are commonly modeled as submodular functions. Submodular (function) maximization is generally NP-hard,…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
We study revenue maximization in multi-item multi-bidder auctions under the natural item-independence assumption - a classical problem in Multi-Dimensional Bayesian Mechanism Design. One of the biggest challenges in this area is developing…
Following the work of Anily et al., we consider a variant of bin packing, called "bin packing with general cost structures" (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic…
We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…
In this paper, we propose and study the cascade submodular maximization problem under the adaptive setting. The input of our problem is a set of items, each item is in a particular state (i.e., the marginal contribution of an item) which is…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
This paper studies the robust optimal gain selection problem for financial trading systems, formulated within a \emph{double linear policy} framework, which allocates capital across long and short positions. The key objective is to…
We consider a variable selection problem for the prediction of binary outcomes. We study the best subset selection procedure by which the covariates are chosen by maximizing Manski (1975, 1985)'s maximum score objective function subject to…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
The multiple knapsack problem with grouped items aims to maximize rewards by assigning groups of items among multiple knapsacks, considering knapsack capacities. Either all items in a group are assigned or none at all. We propose algorithms…
The interval subset sum problem (ISSP) is a generalization of the well-known subset sum problem. Given a set of intervals $\left\{[a_{i,1},a_{i,2}]\right\}_{i=1}^n$ and a target integer $T,$ the ISSP is to find a set of integers, at most…