Related papers: Improved approximation for two dimensional strip p…
We revisit the classic 0-1-Knapsack problem, in which we are given $n$ items with their weights and profits as well as a weight budget $W$, and the goal is to find a subset of items of total weight at most $W$ that maximizes the total…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
We study the approximability of the NP-complete \textsc{Maximum Minimal Feedback Vertex Set} problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type:…
Given a complete graph with $n$ vertices and non-negative edge weights, where $n$ is divisible by 3, the maximum weight 3-path packing problem is to find a set of $n/3$ vertex-disjoint 3-paths such that the total weight of the 3-paths in…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
We study the weighted $k$-Set Packing problem: Given a collection $S$ of sets, each of cardinality at most $k$, together with a positive weight function $w:\mathcal{S}\rightarrow\mathbb{Q}_{>0}$, the task is to compute a disjoint…
In Asymmetric A Priori TSP (with independent activation probabilities) we are given an instance of the Asymmetric Traveling Salesman Problem together with an activation probability for each vertex. The task is to compute a tour that…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
$\delta$-Covering, for some covering range $\delta>0$, is a continuous facility location problem on undirected graphs where all edges have unit length. The facilities may be positioned on the vertices as well as on the interior of the…
We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…
A bicriteria approximation algorithm is presented for the unrooted traveling repairman problem, realizing increased profit in return for increased speedup of repairman motion. The algorithm generalizes previous results from the case in…
We consider the classic scheduling problem of minimizing the total weighted flow-time on a single machine (min-WPFT), when preemption is allowed. In this problem, we are given a set of $n$ jobs, each job having a release time $r_j$, a…
We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have…
We consider approximating analytic functions on the interval $[-1,1]$ from their values at a set of $m+1$ equispaced nodes. A result of Platte, Trefethen \& Kuijlaars states that fast and stable approximation from equispaced samples is…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
We consider a variant of the classical Bin Packing Problem, called Fully Dynamic Bin Packing. In this variant, items of a size in $(0,1]$ must be packed in bins of unit size. In each time step, an item either arrives or departs from the…
In the Closest String problem one is given a family $\mathcal S$ of equal-length strings over some fixed alphabet, and the task is to find a string $y$ that minimizes the maximum Hamming distance between $y$ and a string from $\mathcal S$.…
This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate, the question we study, let us consider the Set-Cover problem with n elements and m…
Best-Fit is one of the most prominent and practically used algorithms for the bin packing problem, where a set of items with associated sizes needs to be packed in the minimum number of unit-capacity bins. Kenyon [SODA '96] studied online…