We propose an embedded attribute encoding method for point clouds based on set partitioning in hierarchical trees (SPIHT). The encoder is used with the region-adaptive transform, which has been a popular transform cloud coding and included standard geometry-based coder (G-PCC). result that efficient, scalable, embedded. That is, higher compression achieved by trimming full bit-stream. G-PCC's R...

Dual heuristics have been successfully used to generate bounds in the context of branch and bound algorithms. In the current work, we present a new dual heuristic for the set partitioning problem. Our approach provides a lower bound at each node of the branch and bound tree by calculating approximate solutions to the dual of the linear relaxation of the set partitioning problem. The calculation...

The Vehicle Positioning Problem (VPP), also know as the shunting problem, is a classical combinatorial optimization problem in public transport planning. It has been investigated using several models and approaches, which work well for small instances, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation approach for the VPP and f...

This paper investigates the potential of constraint programming for solving set partitioning problems occurring in crew scheduling, where constraint programming is restricted to not employ external solvers, as for instance integer linear programming solvers. We evaluate preprocessing steps known from the OR literature on moderately sized set partitioning problems. Further, we propose a new prep...

In this paper, we consider the set partitioning polytope and we begin by applying the reformulation-linearization technique of Sherali and Adams (1990, 1994) to generate a specialized hierarchy of relaxations by exploiting the structure of this polytope. We then show that several known classes of valid inequalities for this polytopc, as well as related tightening and composition rules, are auto...

We consider some constrained partitioning problems for a finite set of objects of different types. We look for partitions that are sizeand type-similar, and, in addition, for a pair of such partitions that are “very different” in a certain sense. The motivation stems from a problem involving the partitioning of a set of students into smaller groups. We give these problems precise mathematical f...

Based on the in-depth analysis of the essence and features of vague phenomena, this paper focuses on establishing the axiomatical foundation of membership degree theory for vague phenomena, presents an axiomatic system to govern membership degrees and their interconnections. On this basis, the concept of vague partition is introduced, further, the concept of fuzzy set introduced by Zadeh in 196...

The Random Projection Tree (RPTREE) structures proposed in [1] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTREE-MAX and the RPTREE-MEAN data structures. Our result for RPTREE-MAX gives a nearoptimal bound on the number of levels required by this data structure to reduce the size of it...

Increasing competition in the air transport market has intensified active airlines’ efforts to keep their market share by attaching due importance to cost management aimed at reduced final prices. Crew costs are second only to fuel costs on the cost list of airline companies. So, this paper attempts to investigate the cockpit crew pairing problem. The set partitioning problem has been used for ...