Related papers: The Incremental Knapsack Problem with Monotone Sub…
The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs. However, it is still an open question whether a sequentially lifted cover inequality can be computed in polynomial time for a given…
The Knapsack problem is one of the most fundamental NP-complete problems at the intersection of computer science, optimization, and operations research. A recent line of research worked towards understanding the complexity of…
The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
We discuss a variant of multitask n-vehicle exploration problem. Instead of requiring an optimal permutation of vehicles in every group, the new problem asks all vehicles in a group to arrive at a same destination. It can also be viewed as…
This paper studies the multi-item newsvendor problem with a constrained budget and information about demand limited to its range, mean and mean absolute deviation. We consider a minimax model that determines order quantities by minimizing…
In this paper the following selection problem is discussed. A set of $n$ items is given and we wish to choose a subset of exactly $p$ items of the minimum total cost. This problem is a special case of 0-1 knapsack in which all the item…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
Finding diverse solutions to optimization problems has been of practical interest for several decades, and recently enjoyed increasing attention in research. While submodular optimization has been rigorously studied in many fields, its…
Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…
Submodularity is one of the most important properties in combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of a $k$-submodular function requires an exponential number of value oracle…
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…
In the knapsack problems with neighborhood constraints that were studied before, the input is a graph $\mathcal{G}$ on a set $\mathcal{V}$ of items, each item $v \in \mathcal{V}$ has a weight $w_v$ and profit $p_v$, the size $s$ of the…
Maximizing the revenue from selling two or more goods has been shown to require the use of $nonmonotonic$ mechanisms, where a higher-valuation buyer may pay less than a lower-valuation one. Here we show that the restriction to $monotonic$…
Knapsack and Partition are two important additive problems whose fine-grained complexities in the $(1-\varepsilon)$-approximation setting are not yet settled. In this work, we make progress on both problems by giving improved algorithms. -…
Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
In this paper, we study the linear complementarity problems on the monotone extended second order cones. We demonstrate that the linear complementarity problem on the monotone extended second order cone can be converted into a mixed…
In this paper, we propose a robust optimization-based heuristic algorithm for the chance-constrained binary knapsack problem (CKP). We assume that the weights of items are independent normally distributed. By utilizing the properties of the…
Recently knapsack problems have been generalized from the integers to arbitrary finitely generated groups. The knapsack problem for a finitely generated group $G$ is the following decision problem: given a tuple $(g, g_1, \ldots, g_k)$ of…