相关论文: Asymptotic Results for the Queen Packing Problem
As the main problem, we consider covering of a $d$-dimensional cube by $n$ balls with reasonably large $d$ (10 or more) and reasonably small $n$, like $n=100$ or $n=1000$. We do not require the full coverage but only 90\% or 95\% coverage.…
In this paper, we present a QUBO formulation designed to solve a series of generalisations of the LinkedIn queens game, a version of the N-queens problem, for the Takuzu game (or Binairo), for the most recent LinkedIn game, Tango, and for…
We consider the Ordered Open End Bin Packing problem. Items of sizes in $(0,1]$ are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size strictly below $1$. This…
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…
We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time. The objective is to pack these items as…
We study several variations of line segment covering problem with axis-parallel unit squares in $I\!\!R^2$. A set $S$ of $n$ line segments is given. The objective is to find the minimum number of axis-parallel unit squares which cover at…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to…
This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide…
Algorithms for triangle-finding, the smallest nontrivial instance of the k-clique problem, have been proposed for quantum computers. Still, those algorithms assume the use of fixed access time quantum RAM (QRAM). We present a practical…
In the packing-constrained point covering problem, PC^2, one seeks configurations of points in the plane that cannot all be covered by a packing arrangement of unit disks. We consider in particular the problem of finding the minimum number…
This paper deals with a variation of the classical isoperimetric problem in dimension $N\ge 2$ for a two-phase piecewise constant density whose discontinuity interface is a given hyperplane. We introduce a weighted perimeter functional with…
An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into \emph{bundles}. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between…
We consider multiwinner elections in Euclidean space using the minimax Chamberlin-Courant rule. In this setting, voters and candidates are embedded in a $d$-dimensional Euclidean space, and the goal is to choose a committee of $k$…
Cardinality constrained bin packing or bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k \geq 2, items having sizes in (0,1] associated with them are presented one by one to…
We prove a tight quantum query lower bound $\Omega(n^{k/(k+1)})$ for the problem of deciding whether there exist $k$ numbers among $n$ that sum up to a prescribed number, provided that the alphabet size is sufficiently large. This is an…
We introduce a two-player game in which one and his/her opponent attempt to pack as many ``prisoners'' as possible on the squares of an n-by-n checkerboard; each prisoner has to be ``protected'' by at least as many guards as the number of…
To count the number of maximum independent arrangements of $n^2$ kings on a $2n\times 2n$ chessboard, we build a $2^n \times (n+1)$ matrix whose entries are independent arrangements of $n$ kings on $2\times 2n$ rectangles. Utilizing upper…
We study a natural generalization of the classical \textsc{Dominating Set} problem, called \textsc{Dominating Set with Quotas} (DSQ). In this problem, we are given a graph \( G \), an integer \( k \), and for each vertex \( v \in V(G) \), a…
A one-dimensional quantum system with off diagonal disorder, consisting of a sample of conducting regions randomly interspersed within potential barriers is considered. Results mainly concerning the large $N$ limit are presented. In…