Related papers: Combinatorial optimization over two random point s…
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…
Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and…
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…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
For the set of graphs with a given degree sequence, consisting of any number of $2's$ and $1's$, and its subset of bipartite graphs, we characterize the optimal graphs who maximize and minimize the number of $m$-matchings. We find the…
For decision making under uncertainty, min-max regret has been established as a popular methodology to find robust solutions. In this approach, we compare the performance of our solution against the best possible performance had we known…
Combinatorial optimization problems play crucial roles in real-world applications, and many studies from a physics perspective have contributed to specialized hardware for high-speed computation. However, some combinatorial optimization…
We consider a set of Euclidean optimization problems in one dimension, where the cost function associated to the couple of points $x$ and $y$ is the Euclidean distance between them to an arbitrary power $p\ge1$, and the points are chosen at…
We study bipartite maps on the plane with one infinite face and one face of perimeter 2. At first we consider the problem of their enumeration an then study the connection between the combinatorial structure of a map and the degree of its…
Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of…
We study a cardinality-constrained optimization problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly we study some properties on the optimal solutions of this optimization problem under…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdos and Renyi about perfect matchings in random bipartite graphs.…
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 present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with…
We consider hypergraphs on vertices $P\cup R$ where each hyperedge contains exactly one vertex in $P$. Our goal is to select a matching that covers all of $P$, but we allow each selected hyperedge to drop all but an $(1/\alpha)$-fraction of…
In a random model of minimum cost bipartite matching based on exponentially distributed edge costs, we show that the distribution of the cost of the optimal solution can be computed efficiently. The distribution is represented by its moment…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…