On a Geometric Approach to the Segment Sum Problem and Its Generalization
نویسندگان
چکیده
Given a sequence of n real numbers a1, a2, a3, . . . , an, the maximum segment sum problem is that of determining indices i and j (1 ≤ i ≤ j ≤ n) such that the sum s(i, j) = ai + ai+1 + . . . + aj is a maximum. Monotone matrices were shown to be remarkably effective in solving several geometric optimization problems. The surprise is that it can also be applied to the above problem as we show here. Recently, there was a breakthrough in obtaining an O(n log n) algorithm for the kth smallest segment sum problem by exploiting a connection of this problem to the well-known slope selection problem. In this paper we show that this problem can also be solved within the same time bounds in the simpler framework of expander graphs.
منابع مشابه
A goal geometric programming problem (G2P2) with logarithmic deviational variables and its applications on two industrial problems
A very useful multi-objective technique is goal programming. There are many methodologies of goal programming such as weighted goal programming, min-max goal programming, and lexicographic goal programming. In this paper, weighted goal programming is reformulated as goal programming with logarithmic deviation variables. Here, a comparison of the proposed method and goal programming with weighte...
متن کاملمدلسازی صفحهای محیطهای داخلی با استفاده از تصاویر RGB-D
In robotic applications and especially 3D map generation of indoor environments, analyzing RGB-D images have become a key problem. The mapping problem is one of the most important problems in creating autonomous mobile robots. Autonomous mobile robots are used in mine excavation, rescue missions in collapsed buildings and even planets’ exploration. Furthermore, indoor mapping is beneficial in f...
متن کاملرفع اعوجاج هندسی متون بهکمک اطلاعات هندسی خطوط متن
Document images produced by scanners or digital cameras usually have photometric and geometric distortions. If either of these effects distorts document, recognition of words from such a document image using OCR is subject to errors. In this paper we propose a novel approach to significantly remove geometric distortion from document images. In this method first we extract document lines from do...
متن کاملVehicle Routing Problem in Competitive Environment: Two-Person Nonzero Sum Game Approach
Vehicle routing problem is one of the most important issues in transportation. Among VRP problems, the competitive VRP is more important because there is a tough competition between distributors and retailers. In this study we introduced new method for VRP in competitive environment. In these methods Two-Person Nonzero Sum games are defined to choose equilibrium solution. Therefore, revenue giv...
متن کاملA hierarchical approach for designing the downstream segment for a supply chain of petroleum production systems
Strategic decisions in a supply chain are the most important decisions for petroleum production systems. These decisions, due to high costs of transportation and storing, are costly and affected by the tactical and operational decisions in uncertain situations. In this article, we focus on designing a downstream segment for a supply chain of petroleum production systems. For this purpose, we wi...
متن کامل