Related papers: Improved approximation for 3-dimensional matching …
In this paper we propose an improved approximation scheme for the Vector Bin Packing problem (VBP), based on the combination of (near-)optimal solution of the Linear Programming (LP) relaxation and a greedy (modified first-fit) heuristic.…
The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in…
We consider the problem of subset selection for $\ell_{p}$ subspace approximation, i.e., given $n$ points in $d$ dimensions, we need to pick a small, representative subset of the given points such that its span gives $(1+\epsilon)$…
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…
An efficient algorithm to solve the $k$ shortest non-homotopic path planning ($k$-SNPP) problem in a 2D environment is proposed in this paper. Motivated by accelerating the inefficient exploration of the homotopy-augmented space of the 2D…
We study a natural geometric variant of the classic Knapsack problem called 2D-Knapsack: we are given a set of axis-parallel rectangles and a rectangular bounding box, and the goal is to pack as many of these rectangles inside the box…
We study the {\em maximum duo-preservation string mapping} ({\sc Max-Duo}) problem, which is the complement of the well studied {\em minimum common string partition} ({\sc MCSP}) problem. Both problems have applications in many fields…
Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We…
We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local search algorithm yields a \PTAS. For the weighted case,…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
In the Multiple Allocation $k$-Hub Center (MA$k$HC), we are given a connected edge-weighted graph $G$, sets of clients $\mathcal{C}$ and hub locations $\mathcal{H}$, where ${V(G) = \mathcal{C} \cup \mathcal{H}}$, a set of demands…
We consider a class of pattern matching problems where a normalising transformation is applied at every alignment. Normalised pattern matching plays a key role in fields as diverse as image processing and musical information processing…
Given a directed graph $G = (V, E)$, the $k$-path partition problem is to find a minimum collection of vertex-disjoint directed paths each of order at most $k$ to cover all the vertices of $V$. The problem has various applications in…
Parameterized Inapproximability Hypothesis (PIH) is a central question in the field of parameterized complexity. PIH asserts that given as input a 2-CSP on $k$ variables and alphabet size $n$, it is W[1]-hard parameterized by $k$ to…
We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian…
We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…
We consider the task of fitting low-dimensional embeddings to high-dimensional data. In particular, we study the $k$-Euclidean Metric Violation problem ($\textsf{$k$-EMV}$), where the input is $D \in \mathbb{R}^{\binom{n}{2}}_{\geq 0}$ and…
Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…
Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \times B$ so that any point of $A \cup B$ appears in…