Related papers: Efficient Locally Optimal Number Set Partitioning …
Given a sequence of $N$ positive real numbers $\{a_1,a_2,..., a_N \}$, the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is…
We model the societal task of redistricting political districts as a partitioning problem: Given a set of $n$ points in the plane, each belonging to one of two parties, and a parameter $k$, our goal is to compute a partition $\Pi$ of the…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
We consider a memory allocation problem that can be modeled as a version of bin packing where items may be split, but each bin may contain at most two (parts of) items. A 3/2-approximation algorithm and an NP-hardness proof for this problem…
In this thesis, we settle the computational complexity of some fundamental questions in polynomial optimization. These include the questions of (i) finding a local minimum, (ii) testing local minimality of a point, and (iii) deciding…
Given a graph $G = (V, E)$, the $3$-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most $3$ to cover all the vertices of $V$. It is different from but closely related to the well-known…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
Due to the significant increase in the size of spatial data, it is essential to use distributed parallel processing systems to efficiently analyze spatial data. In this paper, we first study learned spatial data partitioning, which…
We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
This paper considers the arbitrary-proportional finite-set-partitioning problem which involves partitioning a finite set into multiple subsets with respect to arbitrary nonnegative proportions. This is the core art of many fundamental…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…