Related papers: Maximum Segment Sum, Monadically (distilled tutori…
Semantic image segmentation is an important computer vision task that is difficult because it consists of both recognition and segmentation. The task is often cast as a structured output problem on an exponentially large output-space, which…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
We consider the problem of maximizing the sum of a monotone submodular function and a linear function subject to a general solvable polytope constraint. Recently, Sviridenko et al. (2017) described an algorithm for this problem whose…
To partition a sequence of n integers into subsets with prescribed sums is an NP-hard problem in general. In this paper we present an efficient solution for the homogeneous version of this problem; i.e. where the elements in each subset add…
It is known that the maximum cardinality cut problem is NP-hard even in chordal graphs. In this paper, we consider the time complexity of the problem in proper interval graphs, a subclass of chordal graphs, and propose a dynamic programming…
Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series.…
We study the computational complexity of one of the particular cases of the knapsack problem: the subset sum problem. For solving this problem we consider one of the basic variants of the Branch-and-Bound method in which any sub-problem is…
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
The Maximum Balanced Subgraph Problem (MBSP) is the problem of finding a subgraph of a signed graph that is balanced and maximizes the cardinality of its vertex set. We are interested in the exact solution of the problem: an improved…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…
This paper describes a linear-time algorithm that finds the longest stretch in a sequence of real numbers (``scores'') in which the sum exceeds an input parameter. The algorithm also solves the problem of finding the longest interval in…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal…
The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k…
In this paper, we study the "sum composition problem" between two lists $A$ and $B$ of positive integers. We start by saying that $B$ is "sum composition" of $A$ when there exists an ordered $m$-partition $[A_1,\ldots,A_m]$ of $A$ where $m$…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…