Related papers: The Subset Sum Matching Problem
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
We consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a $2$-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an…
In this paper we study the subset sum problem with real numbers. Starting from the given problem, we formulate a quadratic maximization problem over a polytope which is eventually written as a distance maximization to a fixed point. For…
The paper addresses a new class of combinatorial problems which consist in restructuring of solutions (as structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
We consider the problem of minimizing a sum of $n$ functions over a convex parameter set $\mathcal{C} \subset \mathbb{R}^p$ where $n\gg p\gg 1$. In this regime, algorithms which utilize sub-sampling techniques are known to be effective. In…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
Target tracking faces the challenge in coping with large volumes of data which requires efficient methods for real time applications. The complexity considered in this paper is when there is a large number of measurements which are required…
Boolean Satisfiability (SAT) is arguably the archetypical NP-complete decision problem. Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years. However, many practical uses of…
In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…
This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
Finding the optimal ordering of k-subsets with respect to an objective function is known to be an extremely challenging problem. In this paper we introduce a new objective for this task, rooted in the problem of star identification on…
For $S \in \mathbb{N}^n$ and $T \in \mathbb{N}$, the Subset Sum Problem (SSP) $\exists^? x \in \{0,1\}^n $ such that $S^T\cdot x = T$ can be interpreted as the problem of deciding whether the intersection of the positive unit hypercube $Q_n…
The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…
Given $(a_1, \dots, a_n, t) \in \mathbb{Z}_{\geq 0}^{n + 1}$, the Subset Sum problem ($\mathsf{SSUM}$) is to decide whether there exists $S \subseteq [n]$ such that $\sum_{i \in S} a_i = t$. There is a close variant of the $\mathsf{SSUM}$,…