arXiv subjects

Peter Kling

Publications and source records attributed to Peter Kling.

At least 19 recordsLinked to original sources

arXiv2026

Entangled photons from para-positronium decay: Do coincidences from scattered photons imply a Bell state?

Electron and positron can form a meta-stable bound state called positronium that decays via pair annihilation. We show how polarization-dependent Compton scattering can be used to verify that the two annihilation photons in the spin-zero case (para-positronium) are emitted in a maximally entangled Bell state. Our theoretical approach based on two-photon density matrices connects concepts from relativistic quantum electrodynamics and quantum information theory.

quant-ph↗

arXiv2025

(Almost) Perfect Discrete Iterative Load Balancing

We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually each node has approximately the same number of tokens. We present results for a general class of simple local balancing schemes where the tokens are balanced via matchings. In each round the process averages the tokens of any two matched nodes. If the sum of their tokens is odd, the node to receive the one excess token is selected at random. Our class covers three popular models: in the matching model a new matching is generated randomly in each round, in the balancing circuit model a fixed sequence of matchings is applied periodically, and in the asynchronous model the load is balanced over a randomly chosen edge. We measure the quality of a load vector by its discrepancy, defined as the difference between the maximum and minimum load across all nodes. As our main result we show that with high probability our discrete balancing scheme reaches a discrepancy of $3$ in a number of rounds which asymptotically matches the spectral bound for continuous load balancing with fractional load. This result improves and tightens a long line of previous works, by not only achieving a small constant discrepancy (instead of a non-explicit, large constant) but also holding for arbitrary instead of regular graphs. The result also demonstrates that in the general model we consider, discrete load balancing is no harder than continuous load balancing.

cs.DC↗

arXiv2025

Balls and Bins and the Infinite Process with Random Deletions

We consider an infinite balls-into-bins process with deletions where in each discrete step $t$ a coin is tossed as to whether, with probability $\beta(t) \in (0,1)$, a new ball is allocated using the Greedy[2] strategy (which places the ball in the lower loaded of two bins sampled uniformly at random) or, with remaining probability $1-\beta(t)$, a ball is deleted from a non-empty bin chosen uniformly at random. Let $n$ be the number of bins and $m(t)$ the total load at time $t$. We are interested in bounding the discrepancy $x_{\max}(t) - m(t)/n$ (current maximum load relative to current average) and the overload $x_{\max}(t) - m_{\max}(t)/n$ (current maximum load relative to highest average observed so far). We prove that at an arbitrarily chosen time $t$ the total number of balls above the average is $O(n)$ and that the discrepancy is $ O(\log(n))$. For the discrepancy, we provide a matching lower bound. Furthermore we prove that at an arbitrarily chosen time $t$ the overload is $\log\log(n)+O(1)$. For "good" insertion probability sequences (in which the average load of time intervals with polynomial length increases in expectation) we show that even the discrepancy is bounded by $\log\log(n)+O(1)$. One of our main analytical tools is a layered induction, as per [ABKU99]. Since our model allows for rather more general scenarios than what was previously considered, the formal analysis requires some extra ingredients as well, in particular a detailed potential analysis. Furthermore, we simplify the setup by applying probabilistic couplings to obtain certain "recovery" properties, which eliminate much of the need for intricate and careful conditioning elsewhere in the analysis.

cs.DC↗

arXiv2024

Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility

In the general pattern formation (GPF) problem, a swarm of simple autonomous, disoriented robots must form a given pattern. The robots' simplicity imply a strong limitation: When the initial configuration is rotationally symmetric, only patterns with a similar symmetry can be formed [Yamashita, Suzyuki; TCS 2010]. The only known algorithm to form large patterns with limited visibility and without memory requires the robots to start in a near-gathering (a swarm of constant diameter) [Hahn et al.; SAND 2024]. However, not only do we not know any near-gathering algorithm guaranteed to preserve symmetry but most natural gathering strategies trivially increase symmetries [Castenow et al.; OPODIS 2022]. Thus, we study near-gathering without changing the swarm's rotational symmetry for disoriented, oblivious robots with limited visibility (the OBLOT-model, see [Flocchini et al.; 2019]). We introduce a technique based on the theory of dynamical systems to analyze how a given algorithm affects symmetry and provide sufficient conditions for symmetry preservation. Until now, it was unknown whether the considered OBLOT-model allows for any non-trivial algorithm that always preserves symmetry. Our first result shows that a variant of Go-to-the-Average always preserves symmetry but may sometimes lead to multiple, unconnected near-gathering clusters. Our second result is a symmetry-preserving near-gathering algorithm that works on swarms with a convex boundary (the outer boundary of the unit disc graph) and without holes (circles of diameter 1 inside the boundary without any robots).

cs.RO↗

arXiv2024

Quantum free-electron laser oscillator

If the quantum mechanical recoil of the electron due to its scattering from the undulator and laser fields dominates the dynamics, a regime of the free-electron laser emerges where quantum effects lead to a drastic change in the radiation properties. However, the large interaction length required for a single-pass quantum free-electron laser impedes the experimental realization. The quantum free-electron laser oscillator, proposed in the present article, is a possible scheme to resolve this issue. Here we show that this device features a photon statistics that is closer to a coherent state in comparison to existing classical free-electron lasers. The device can be even operated in such a way that a sub-Poissonian statistics is obtained. Beside the benefit of demonstrating this pure quantum effect, the narrowing of the photon distribution implies reduced intensity fluctuations of the emitted radiation, which in turn lead to decreased noise in imaging experiments or to an enhanced sensitivity in interferometric applications.

quant-ph↗

arXiv2024

Forming Large Patterns with Local Robots in the OBLOT Model

In the arbitrary pattern formation problem, $n$ autonomous, mobile robots must form an arbitrary pattern $P \subseteq \mathbb{R}^2$. The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to communicate. An important distinction is whether robots have memory and/or a limited viewing range. Previous work managed to form $P$ under a natural symmetry condition if robots have no memory but an unlimited viewing range [22] or if robots have a limited viewing range but memory [25]. In the latter case, $P$ is only formed in a shrunk version that has constant diameter. Without memory and with limited viewing range, forming arbitrary patterns remains an open problem. We provide a partial solution by showing that $P$ can be formed under the same symmetry condition if the robots' initial diameter is $\leq 1$. Our protocol partitions $P$ into rotation-symmetric components and exploits the initial mutual visibility to form one cluster per component. Using a careful placement of the clusters and their robots, we show that a cluster can move in a coordinated way through its component while drawing $P$ by dropping one robot per pattern coordinate.

cs.RO↗

arXiv2024

Population Protocols for Exact Plurality Consensus -- How a small chance of failure helps to eliminate insignificant opinions

We consider the \emph{exact plurality consensus} problem for \emph{population protocols}. Here, $n$ anonymous agents start each with one of $k$ opinions. Their goal is to agree on the initially most frequent opinion (the \emph{plurality opinion}) via random, pairwise interactions. The case of $k = 2$ opinions is known as the \emph{majority problem}. Recent breakthroughs led to an always correct, exact majority population protocol that is both time- and space-optimal, needing $O(\log n)$ states per agent and, with high probability, $O(\log n)$ time~[Doty, Eftekhari, Gasieniec, Severson, Stachowiak, and Uznanski; 2021]. We know that any always correct protocol requires $\Omega(k^2)$ states, while the currently best protocol needs $O(k^{11})$ states~[Natale and Ramezani; 2019]. For ordered opinions, this can be improved to $O(k^6)$~[Gasieniec, Hamilton, Martin, Spirakis, and Stachowiak; 2016]. We design protocols for plurality consensus that beat the quadratic lower bound by allowing a negligible failure probability. While our protocols might fail, they identify the plurality opinion with high probability even if the bias is $1$. Our first protocol achieves this via $k-1$ tournaments in time $O(k \cdot \log n)$ using $O(k + \log n)$ states. While it assumes an ordering on the opinions, we remove this restriction in our second protocol, at the cost of a slightly increased time $O(k \cdot \log n + \log^2 n)$. By efficiently pruning insignificant opinions, our final protocol reduces the number of tournaments at the cost of a slightly increased state complexity $O(k \cdot \log\log n + \log n)$. This improves the time to $O(n / x_{\max} \cdot \log n + \log^2 n)$, where $x_{\max}$ is the initial size of the plurality. Note that $n/x_{\max}$ is at most $k$ and can be much smaller (e.g., in case of a large bias or if there are many small opinions).

cs.DC↗

arXiv2023

Improved Scheduling with a Shared Resource

We consider the following shared-resource scheduling problem: Given a set of jobs $J$, for each $j\in J$ we must schedule a job-specific processing volume of $v_j>0$. A total resource of $1$ is available at any time. Jobs have a resource requirement $r_j\in[0,1]$, and the resources assigned to them may vary over time. However, assigning them less will cause a proportional slowdown. We consider two settings. In the first, we seek to minimize the makespan in an online setting: The resource assignment of a job must be fixed before the next job arrives. Here we give an optimal $e/(e-1)$-competitive algorithm with runtime $\mathcal{O}(n\cdot \log n)$. In the second, we aim to minimize the total completion time. We use a continuous linear programming (CLP) formulation for the fractional total completion time and combine it with a previously known dominance property from malleable job scheduling to obtain a lower bound on the total completion time. We extract structural properties by considering a geometrical representation of a CLP's primal-dual pair. We combine the CLP schedule with a greedy schedule to obtain a $(3/2+\varepsilon)$-approximation for this setting. This improves upon the so far best-known approximation factor of $2$.

cs.DS↗

arXiv2023

Scheduling with a Limited Testing Budget

Scheduling with testing falls under the umbrella of the research on optimization with explorable uncertainty. In this model, each job has an upper limit on its processing time that can be decreased to a lower limit (possibly unknown) by some preliminary action (testing). Recently, D{\"{u}}rr et al. \cite{DBLP:journals/algorithmica/DurrEMM20} has studied a setting where testing a job takes a unit time, and the goal is to minimize total completion time or makespan on a single machine. In this paper, we extend their problem to the budget setting in which each test consumes a job-specific cost, and we require that the total testing cost cannot exceed a given budget. We consider the offline variant (the lower processing time is known) and the oblivious variant (the lower processing time is unknown) and aim to minimize the total completion time or makespan on a single machine. For the total completion time objective, we show NP-hardness and derive a PTAS for the offline variant based on a novel LP rounding scheme. We give a $(4+\epsilon)$-competitive algorithm for the oblivious variant based on a framework inspired by the worst-case lower-bound instance. For the makespan objective, we give an FPTAS for the offline variant and a $(2+\epsilon)$-competitive algorithm for the oblivious variant. Our algorithms for the oblivious variants under both objectives run in time $O(poly(n/\epsilon))$. Lastly, we show that our results are essentially optimal by providing matching lower bounds.

cs.DS↗

arXiv2023

Multiphoton processes and higher resonances in the quantum regime of the free-electron laser

Despite exhibiting novel radiation features, the operation of the proposed quantum free-electron laser would have the drawback that the number of emitted photons is limited by one per electron, significantly reducing the output power of such a device. We show that relying on different resonances of the initial momentum of the electrons increases the number of emitted photons, but also increases the required length of the undulator impeding an experimetal realization. Moreover, we investigate how multiphoton processes influence the dynamics in the deep quantum regime.

quant-ph↗

arXiv2023

Moving Target Defense for Service-oriented Mission-critical Networks

Modern mission-critical systems (MCS) are increasingly softwarized and interconnected. As a result, their complexity increased, and so their vulnerability against cyber-attacks. The current adoption of virtualization and service-oriented architectures (SOA) in MCSs provides additional flexibility that can be leveraged to withstand and mitigate attacks, e.g., by moving critical services or data flows. This enables the deployment of strategies for moving target defense (MTD), which allows stripping attackers of their asymmetric advantage from the long reconnaissance of MCSs. However, it is challenging to design MTD strategies, given the diverse threat landscape, resource limitations, and potential degradation in service availability. In this paper, we combine two optimization models to explore feasible service configurations for SOA-based systems and to derive subsequent MTD actions with their time schedule based on an attacker-defender game. Our results indicate that even for challenging and diverse attack scenarios, our models can defend the system by up to 90% of the system operation time with a limited MTD defender budget.

cs.CR↗

arXiv2022

A Unifying Approach to Efficient (Near)-Gathering of Disoriented Robots with Limited Visibility

We consider a swarm of $n$ robots in \mathbb{R}^d. The robots are oblivious, disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task gathering requires that all robots reach the same, not predefined position. In the related near-gathering task, they must reach distinct positions such that every robot sees the entire swarm. In the considered setting, gathering can be solved in $\mathcal{O}(n + \Delta^2)$ synchronous rounds both in two and three dimensions, where $\Delta$ denotes the initial maximal distance of two robots. In this work, we formalize a key property of efficient gathering protocols and use it to define $\lambda$-contracting protocols. Any such protocol gathers $n$ robots in the $d$-dimensional space in $\mathcal{O}(\Delta^2)$ synchronous rounds. Moreover, we prove a corresponding lower bound stating that any protocol in which robots move to target points inside of the local convex hulls of their neighborhoods -- $\lambda$-contracting protocols have this property -- requires $\Omega(\Delta^2)$ rounds to gather all robots. Among others, we prove that the $d$-dimensional generalization of the GtC-protocol is $\lambda$-contracting. Remarkably, our improved and generalized runtime bound is independent of $n$ and $d$. The independence of $d$ answers an open research question. We also introduce an approach to make any $\lambda$-contracting protocol collisionfree to solve near-gathering. The resulting protocols maintain the runtime of $\Theta (\Delta^2)$ and work even in the semi-synchronous model.

cs.DC↗

arXiv2021

High-gain quantum free-electron laser: long-time dynamics and requirements

We solve the long-time dynamics of a high-gain free-electron laser in the quantum regime. In this regime each electron emits at most one photon on average, independently of the initial field. In contrast, the variance of the photon statistics shows a qualitatively different behavior for different initial states of the field. We find that the realization of a seeded Quantum FEL is more feasible than self-amplified spontaneous emission.

quant-ph↗

arXiv2021

Fast Consensus via the Unconstrained Undecided State Dynamics

We consider the plurality consensus problem among $n$ agents. Initially, each agent has one of $k$ different opinions. Agents choose random interaction partners and revise their state according to a fixed transition function, depending on their own state and the state of the interaction partners. The goal is to reach a consensus configuration in which all agents agree on the same opinion, and if there is initially a sufficiently large bias towards one opinion, that opinion should prevail. We analyze a synchronized variant of the undecided state dynamics defined as follows. The agents act in phases, consisting of a decision and a boosting part. In the decision part, any agent that encounters an agent with a different opinion becomes undecided. In the boosting part, undecided agents adopt the first opinion they encounter. We consider this dynamics in the population model and the gossip model. For the population model, our protocol reaches consensus (w.h.p.) in $O(\log^2 n)$ parallel time, providing the first polylogarithmic result for $k > 2$ (w.h.p.) in this model. Without any assumption on the bias, fast consensus has only been shown for $k = 2$ for the unsynchronized version of the undecided state dynamics [Clementi et al., MFCS'18]. We show that the synchronized variant of the undecided state dynamics reaches consensus (w.h.p.) in time $O(\log^2 n)$, independently of the initial number, bias, or distribution of opinions. In both models, we guarantee that if there is an initial bias of $\Omega(\sqrt{n \log n})$, then (w.h.p.) that opinion wins. A simple extension of our protocol in the gossip model yields a dynamics that does not depend on $n$ or $k$, is anonymous, and has (w.h.p.) runtime $O(\log^2 n)$. This solves an open problem formulated by Becchetti et al.~[Distributed Computing,~2017].

cs.DC↗

arXiv2021

On Greedily Packing Anchored Rectangles

Consider a set P of points in the unit square U, one of them being the origin. For each point p in P you may draw a rectangle in U with its lower-left corner in p. What is the maximum area such rectangles can cover without overlapping each other? Freedman [1969] posed this problem in 1969, asking whether one can always cover at least 50% of U. Over 40 years later, Dumitrescu and T\'oth [2011] achieved the first constant coverage of 9.1%; since then, no significant progress was made. While 9.1% might seem low, the authors could not find any instance where their algorithm covers less than 50%, nourishing the hope to eventually prove a 50% bound. While we indeed significantly raise the algorithm's coverage to 39%, we extinguish the hope of reaching 50% by giving points for which the coverage is below 43.3%. Our analysis studies the algorithm's average and worst-case density of so-called tiles, which represent the area where a given point can freely choose its maximum-area rectangle. Our approachis comparatively general and may potentially help in analyzing related algorithms.

cs.CG↗

arXiv2020

On Minimum Generalized Manhattan Connections

We consider minimum-cardinality Manhattan connected sets with arbitrary demands: Given a collection of points $P$ in the plane, together with a subset of pairs of points in $P$ (which we call demands), find a minimum-cardinality superset of $P$ such that every demand pair is connected by a path whose length is the $\ell_1$-distance of the pair. This problem is a variant of three well-studied problems that have arisen in computational geometry, data structures, and network design: (i) It is a node-cost variant of the classical Manhattan network problem, (ii) it is an extension of the binary search tree problem to arbitrary demands, and (iii) it is a special case of the directed Steiner forest problem. Since the problem inherits basic structural properties from the context of binary search trees, an $O(\log n)$-approximation is trivial. We show that the problem is NP-hard and present an $O(\sqrt{\log n})$-approximation algorithm. Moreover, we provide an $O(\log\log n)$-approximation algorithm for complete bipartite demands as well as improved results for unit-disk demands and several generalizations. Our results crucially rely on a new lower bound on the optimal cost that could potentially be useful in the context of BSTs.

cs.DS↗

arXiv2020

A Discrete and Continuous Study of the Max-Chain-Formation Problem

Most existing robot formation problems seek a target formation of a certain \emph{minimal} and, thus, efficient structure. Examples include the Gathering and the Chain-Formation problem. In this work, we study formation problems that try to reach a \emph{maximal} structure, supporting for example an efficient coverage in exploration scenarios. A recent example is the NASA Shapeshifter project, which describes how the robots form a relay chain along which gathered data from extraterrestrial cave explorations may be sent to a home base. As a first step towards understanding such maximization tasks, we introduce and study the Max-Chain-Formation problem, where $n$ robots are ordered along a winding, potentially self-intersecting chain and must form a connected, straight line of maximal length connecting its two endpoints. We propose and analyze strategies in a discrete and in a continuous time model. In the discrete case, we give a complete analysis if all robots are initially collinear, showing that the worst-case time to reach an $\varepsilon$-approximation is upper bounded by $\mathcal{O}(n^2 \cdot \log (n/\varepsilon))$ and lower bounded by $\Omega(n^2 \cdot~\log (1/\varepsilon))$. If one endpoint of the chain remains stationary, this result can be extended to the non-collinear case. If both endpoints move, we identify a family of instances whose runtime is unbounded. For the continuous model, we give a strategy with an optimal runtime bound of $\Theta(n)$. Avoiding an unbounded runtime similar to the discrete case relies crucially on a counter-intuitive aspect of the strategy: slowing down the endpoints while all other robots move at full speed. Surprisingly, we can show that a similar trick does not work in the discrete model.

cs.DC↗

arXiv2019

Quantum and classical phase-space dynamics of a free-electron laser

In a quantum mechanical description of the free-electron laser (FEL) the electrons jump on discrete momentum ladders, while they follow continuous trajectories according to the classical description. In order to observe the transition from quantum to classical dynamics, it is not sufficient that many momentum levels are involved. Only if additionally the initial momentum spread of the electron beam is larger than the quantum mechanical recoil, caused by the emission and absorption of photons, the quantum dynamics in phase space resembles the classical one. Beyond these criteria, quantum signatures of averaged quantities like the FEL gain might be washed out.

quant-ph↗