arXiv subjects

Daniel Marx

Publications and source records attributed to Daniel Marx.

At least 19 recordsLinked to original sources

arXiv2025

A Collimation System Baseline Design for the Electron Storage Ring at the Electron-Ion Collider

We present the baseline design of the electron ring collimation system for the Electron-Ion Collider (EIC) at Brookhaven National Laboratory (BNL). The system addresses beam losses in a high-current electron storage ring with superconducting (SC) final-focus magnets and sensitive detectors, where uncontrolled losses can generate heat loads, radiation, and detector backgrounds and damage. The proposed collimation insertion localizes halo particle losses through reducing interaction region beam losses from beam-gas and Touschek scattering by several orders of magnitude while keeping detector backgrounds and cryostat heat loads within acceptable limits. Multi-turn particle tracking simulations show that the collimators do not significantly impact machine acceptance or beam lifetime, and their positions and apertures can be re-optimized for future lattice configurations. Ongoing work includes incorporating crab cavities and solenoid fields into simulations, refining vacuum conditions, and optimizing collimator geometry and materials. This design establishes a robust baseline for the EIC electron ring collimation system and supports continued lattice optimization for machine operations.

physics.acc-ph↗

arXiv2025

On Subexponential Parameterized Algorithms for Steiner Tree on Intersection Graphs of Geometric Objects

We study the Steiner Tree problem on the intersection graph of most natural families of geometric objects, e.g., disks, squares, polygons, etc. Given a set of $n$ objects in the plane and a subset $T$ of $t$ terminal objects, the task is to find a subset $S$ of $k$ objects such that the intersection graph of $S\cup T$ is connected. Given how typical parameterized problems behave on planar graphs and geometric intersection graphs, we would expect that exact algorithms with some form of subexponential dependence on the solution size or the number of terminals exist. Contrary to this expectation, we show that, assuming the Exponential-Time Hypothesis (ETH), there is no $2^{o(k+t)}\cdot n^{O(1)}$ time algorithm even for unit disks or unit squares, that is, there is no FPT algorithm subexponential in the size of the Steiner tree. However, subexponential dependence can appear in a different form: we show that Steiner Tree can be solved in time $n^{O(\sqrt{t})}$ for many natural classes of objects, including: Disks of arbitrary size. Axis-parallel squares of arbitrary size. Similarly-sized fat polygons. This in particular significantly improves and generalizes two recent results: (1) Steiner Tree on unit disks can be solved in time $n^{\Oh(\sqrt{k + t})}$ (Bhore, Carmi, Kolay, and Zehavi, Algorithmica 2023) and (2) Steiner Tree on planar graphs can be solved in time $n^{O(\sqrt{t})}$ (Marx, Pilipczuk, and Pilipczuk, FOCS 2018). We complement our algorithms with lower bounds that demonstrate that the class of objects cannot be significantly extended, even if we allow the running time to be $n^{o(k+t)/\log(k+t)}$.

cs.CG↗

arXiv2025

Mapping complex optical light field distributions with single fluorescent molecules

Single fluorescent molecules, behaving as ideal electric dipole emitters, are powerful nanoscopic probes of complex optical fields. Here, this property is exploited to precisely map the polarization and vectorial structure of tightly focused laser beams, utilizing both linear and circular polarization states. The resulting three-dimensional fluorescence excitation maps strikingly reveal the intrinsic chiral and non-chiral structure of the light field, in perfect quantitative agreement with a full vectorial wave-optical model. This precise correspondence not only enables the reliable determination of absolute molecular orientations but also allows for the accurate characterization of the field's properties. These results fundamentally advance our understanding of light-matter interaction at the single-molecule level and open new avenues for characterizing complex light fields, with broad applications in super-resolution microscopy and nanophotonics.

physics.optics↗

arXiv2024

Assessing global crabbing scheme feasibility for Electron-Ion Collider

The Electron-Ion Collider (EIC) plans to utilize the local crabbing crossing scheme. This paper explores the feasibility of adopting a single crab cavity with adjusted voltage, inspired by the successful global crabbing scheme in KEKB, to restore effective head-on collisions. Using weak-strong simulations, the study assesses the potential of this global crabbing scheme for the EIC while emphasizing the need for adiabatic cavity ramping to prevent luminosity loss. Additionally, the research outlines potential risks associated with beam dynamics in implementing this scheme.

physics.acc-ph↗

arXiv2023

Approximate Monotone Local Search for Weighted Problems

In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more generally, parameterized approximation algorithms. In this work, we generalize those results to the weighted setting. More formally, we consider monotone subset minimization problems over a weighted universe of size $n$ (e.g., Vertex Cover, $d$-Hitting Set and Feedback Vertex Set). We consider a model where the algorithm is only given access to a subroutine that finds a solution of weight at most $\alpha \cdot W$ (and of arbitrary cardinality) in time $c^k \cdot n^{O(1)}$ where $W$ is the minimum weight of a solution of cardinality at most $k$. In the unweighted setting, Esmer et al. determine the smallest value $d$ for which a $\beta$-approximation algorithm running in time $d^n \cdot n^{O(1)}$ can be obtained in this model. We show that the same dependencies also hold in a weighted setting in this model: for every fixed $\varepsilon>0$ we obtain a $\beta$-approximation algorithm running in time $O\left((d+\varepsilon)^{n}\right)$, for the same $d$ as in the unweighted setting. Similarly, we also extend a $\beta$-approximate brute-force search (in a model which only provides access to a membership oracle) to the weighted setting. Using existing approximation algorithms and exact parameterized algorithms for weighted problems, we obtain the first exponential-time $\beta$-approximation algorithms that are better than brute force for a variety of problems including Weighted Vertex Cover, Weighted $d$-Hitting Set, Weighted Feedback Vertex Set and Weighted Multicut.

cs.DS↗

arXiv2022

Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: a Complete Classification

In the Directed Steiner Network problem, the input is a directed graph G, a subset T of k vertices of G called the terminals, and a demand graph D on T. The task is to find a subgraph H of G with the minimum number of edges such that for every edge (s,t) in D, the solution H contains a directed s to t path. In this paper we investigate how the complexity of the problem depends on the demand pattern when G is planar. Formally, if \mathcal{D} is a class of directed graphs closed under identification of vertices, then the \mathcal{D}-Steiner Network (\mathcal{D}-SN) problem is the special case where the demand graph D is restricted to be from \mathcal{D}. For general graphs, Feldmann and Marx [ICALP 2016] characterized those families of demand graphs where the problem is fixed-parameter tractable (FPT) parameterized by the number k of terminals. They showed that if \mathcal{D} is a superset of one of the five hard families, then \mathcal{D}-SN is W[1]-hard parameterized by k, otherwise it can be solved in time f(k)n^{O(1)}. For planar graphs an interesting question is whether the W[1]-hard cases can be solved by subexponential parameterized algorithms. Chitnis et al. [SICOMP 2020] showed that, assuming the ETH, there is no f(k)n^{o(k)} time algorithm for the general \mathcal{D}-SN problem on planar graphs, but the special case called Strongly Connected Steiner Subgraph can be solved in time f(k) n^{O(\sqrt{k})} on planar graphs. We present a far-reaching generalization and unification of these two results: we give a complete characterization of the behavior of every $\mathcal{D}$-SN problem on planar graphs. We show that assuming ETH, either the problem is (1) solvable in time 2^{O(k)}n^{O(1)}, and not in time 2^{o(k)}n^{O(1)}, or (2) solvable in time f(k)n^{O(\sqrt{k})}, but not in time f(k)n^{o(\sqrt{k})}, or (3) solvable in time f(k)n^{O(k)}, but not in time f(k)n^{o({k})}.

cs.DS↗

arXiv2022

Domination and Cut Problems on Chordal Graphs with Bounded Leafage

The leafage of a chordal graph G is the minimum integer l such that G can be realized as an intersection graph of subtrees of a tree with l leaves. We consider structural parameterization by the leafage of classical domination and cut problems on chordal graphs. Fomin, Golovach, and Raymond [ESA 2018, Algorithmica 2020] proved, among other things, that Dominating Set on chordal graphs admits an algorithm running in time $2^{O(l^2)} n^{O(1)}$. We present a conceptually much simpler algorithm that runs in time $2^{O(l)} n^{O(1)}$. We extend our approach to obtain similar results for Connected Dominating Set and Steiner Tree. We then consider the two classical cut problems MultiCut with Undeletable Terminals and Multiway Cut with Undeletable Terminals. We prove that the former is W[1]-hard when parameterized by the leafage and complement this result by presenting a simple $n^{O(l)}$-time algorithm. To our surprise, we find that Multiway Cut with Undeletable Terminals on chordal graphs can be solved, in contrast, in $n^{O(1)}$-time.

cs.DS↗

arXiv2019

Almost Tight Lower Bounds for Hard Cutting Problems in Embedded Graphs

We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut problem. A cut graph of a graph $G$ embedded on a surface $S$ is a subgraph of $G$ whose removal from $S$ leaves a disk. We consider the problem of deciding whether an unweighted graph embedded on a surface of genus $g$ has a cut graph of length at most a given value. We prove a time lower bound for this problem of $n^{\Omega(g/\log g)}$ conditionally to ETH. In other words, the first $n^{O(g)}$-time algorithm by Erickson and Har-Peled [SoCG 2002, Discr.\ Comput.\ Geom.\ 2004] is essentially optimal. We also prove that the problem is W[1]-hard when parameterized by the genus, answering a 17-year old question of these authors. A multiway cut of an undirected graph $G$ with $t$ distinguished vertices, called terminals, is a set of edges whose removal disconnects all pairs of terminals. We consider the problem of deciding whether an unweighted graph $G$ has a multiway cut of weight at most a given value. We prove a time lower bound for this problem of $n^{\Omega(\sqrt{gt + g^2+t}/\log(g+t))}$, conditionally to ETH, for any choice of the genus $g\ge0$ of the graph and the number of terminals $t\ge4$. In other words, the algorithm by the second author [Algorithmica 2017] (for the more general multicut problem) is essentially optimal; this extends the lower bound by the third author [ICALP 2012] (for the planar case). Reductions to planar problems usually involve a grid-like structure. The main novel idea for our results is to understand what structures instead of grids are needed if we want to exploit optimally a certain value $g$ of the genus.

cs.CC↗

arXiv2019

Slightly Superexponential Parameterized Problems

A central problem in parameterized algorithms is to obtain algorithms with running time $f(k)\cdot n^{O(1)}$ such that $f$ is as slow growing function of the parameter $k$ as possible. In particular, a large number of basic parameterized problems admit parameterized algorithms where $f(k)$ is single-exponential, that is, $c^k$ for some constant $c$, which makes aiming for such a running time a natural goal for other problems as well. However there are still plenty of problems where the $f(k)$ appearing in the best known running time is worse than single-exponential and it remained ``slightly superexponential'' even after serious attempts to bring it down. A natural question to ask is whether the $f(k)$ appearing in the running time of the best-known algorithms is optimal for any of these problems. In this paper, we examine parameterized problems where $f(k)$ is $k^{O(k)}=2^{O(k\log k)}$ in the best known running time and for a number of such problems, we show that the dependence on $k$ in the running time cannot be improved to single exponential. (See paper for the longer abstract.)

cs.CC↗

arXiv2019

Covering a tree with rooted subtrees

We consider the multiple traveling salesman problem on a weighted tree. In this problem there are $m$ salesmen located at the root initially. Each of them will visit a subset of vertices and return to the root. The goal is to assign a tour to every salesman such that every vertex is visited and the longest tour among all salesmen is minimized. The problem is equivalent to the subtree cover problem, in which we cover a tree with rooted subtrees such that the weight of the maximum weighted subtree is minimized. The classical machine scheduling problem can be viewed as a special case of our problem when the given tree is a star. We observe that, the problem remains NP-hard even if tree height and edge weight are constant, and present an FPT algorithm for this problem parameterized by the largest tour length. To achieve the FPT algorithm, we show a more general result. We prove that, integer linear programming that has a tree-fold structure is in FPT, which extends the FPT result for the $n$-fold integer programming by Hemmecke, Onn and Romanchuk.

cs.DS↗

arXiv2018

The Parameterized Hardness of the k-Center Problem in Transportation Networks

In this paper we study the hardness of the $k$-Center problem on inputs that model transportation networks. For the problem, a graph $G=(V,E)$ with edge lengths and an integer $k$ are given and a center set $C\subseteq V$ needs to be chosen such that $|C|\leq k$. The aim is to minimize the maximum distance of any vertex in the graph to the closest center. This problem arises in many applications of logistics, and thus it is natural to consider inputs that model transportation networks. Such inputs are often assumed to be planar graphs, low doubling metrics, or bounded highway dimension graphs. For each of these models, parameterized approximation algorithms have been shown to exist. We complement these results by proving that the $k$-Center problem is W[1]-hard on planar graphs of constant doubling dimension, where the parameter is the combination of the number of centers $k$, the highway dimension $h$, and the pathwidth $p$. Moreover, under the Exponential Time Hypothesis there is no $f(k,p,h)\cdot n^{o(p+\sqrt{k+h})}$ time algorithm for any computable function $f$. Thus it is unlikely that the optimum solution to $k$-Center can be found efficiently, even when assuming that the input graph abides to all of the above models for transportation networks at once! Additionally we give a simple parameterized $(1+\varepsilon)$-approximation algorithm for inputs of doubling dimension $d$ with runtime $(k^k/\varepsilon^{O(kd)})\cdot n^{O(1)}$. This generalizes a previous result, which considered inputs in $D$-dimensional $L_q$ metrics.

cs.CC↗

arXiv2018

Longitudinal phase space reconstruction simulation studies using a novel X-band transverse deflecting structure at the SINBAD facility at DESY

A transverse deflecting structure (TDS) is a well-known device for characterizing the longitudinal properties of an electron bunch in a linear accelerator. The standard use of such a cavity involves streaking the bunch along a transverse axis and analysing the image on a screen downstream to find the bunch length and slice properties along the other transverse axis. A novel X-band deflecting structure, which will allow the polarization of the deflecting field to be adjusted, is currently being designed as part of a collaboration between CERN, DESY and PSI. This new design will allow bunches to be streaked at any transverse angle within the cavity, which will open up the possibility of new measurement techniques, which could be combined to characterize the 6D phase space distribution of bunches. In this paper, a method is presented for reconstructing the longitudinal phase space distribution of bunches by using the TDS in combination with a dipole. Simulations of this technique for the SINBAD-ARES beamline are presented and the key limitations related to temporal resolution and induced energy spread are discussed.

physics.acc-ph↗

arXiv2017

The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems

Given a directed graph $G$ and a list $(s_1,t_1),\dots,(s_d,t_d)$ of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of $G$ that contains a directed $s_i\to t_i$ path for every $1\le i \le k$. The special case Directed Steiner Tree (when we ask for paths from a root $r$ to terminals $t_1,\dots,t_d$) is known to be fixed-parameter tractable parameterized by the number of terminals, while the special case Strongly Connected Steiner Subgraph (when we ask for a path from every $t_i$ to every other $t_j$) is known to be W[1]-hard. We systematically explore the complexity landscape of directed Steiner problems to fully understand which other special cases are FPT or W[1]-hard. Formally, if $\mathcal{H}$ is a class of directed graphs, then we look at the special case of Directed Steiner Network where the list $(s_1,t_1),\dots,(s_d,t_d)$ of requests form a directed graph that is a member of $\mathcal{H}$. Our main result is a complete characterization of the classes $\mathcal{H}$ resulting in fixed-parameter tractable special cases: we show that if every pattern in $\mathcal{H}$ has the combinatorial property of being "transitively equivalent to a bounded-length caterpillar with a bounded number of extra edges," then the problem is FPT, and it is W[1]-hard for every recursively enumerable $\mathcal{H}$ not having this property. This complete dichotomy unifies and generalizes the known results showing that Directed Steiner Tree is FPT [Dreyfus and Wagner, Networks 1971], $q$-Root Steiner Tree is FPT for constant $q$ [Such\'y, WG 2016], Strongly Connected Steiner Subgraph is W[1]-hard [Guo et al., SIAM J. Discrete Math. 2011], and Directed Steiner Network is solvable in polynomial-time for constant number of terminals [Feldman and Ruhl, SIAM J. Comput. 2006], and moreover reveals a large continent of tractable cases that were not known before.

cs.DS↗

arXiv2016

Constant-factor approximations for asymmetric TSP on nearly-embeddable graphs

In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a closed walk of minimum cost in a directed graph visiting every vertex. We consider the approximability of ATSP on topologically restricted graphs. It has been shown by [Oveis Gharan and Saberi 2011] that there exists polynomial-time constant-factor approximations on planar graphs and more generally graphs of constant orientable genus. This result was extended to non-orientable genus by [Erickson and Sidiropoulos 2014]. We show that for any class of \emph{nearly-embeddable} graphs, ATSP admits a polynomial-time constant-factor approximation. More precisely, we show that for any fixed $k\geq 0$, there exist $\alpha, \beta>0$, such that ATSP on $n$-vertex $k$-nearly-embeddable graphs admits a $\alpha$-approximation in time $O(n^\beta)$. The class of $k$-nearly-embeddable graphs contains graphs with at most $k$ apices, $k$ vortices of width at most $k$, and an underlying surface of either orientable or non-orientable genus at most $k$. Prior to our work, even the case of graphs with a single apex was open. Our algorithm combines tools from rounding the Held-Karp LP via thin trees with dynamic programming. We complement our upper bounds by showing that solving ATSP exactly on graphs of pathwidth $k$ (and hence on $k$-nearly embeddable graphs) requires time $n^{\Omega(k)}$, assuming the Exponential-Time Hypothesis (ETH). This is surprising in light of the fact that both TSP on undirected graphs and Minimum Cost Hamiltonian Cycle on directed graphs are FPT parameterized by treewidth.

cs.DS↗

arXiv2013

List H-Coloring a Graph by Removing Few Vertices

In the deletion version of the list homomorphism problem, we are given graphs G and H, a list L(v) that is a subset of V(H) for each vertex v of G, and an integer k. The task is to decide whether there exists a subset W of V(G) of size at most k such that there is a homomorphism from G \ W to H respecting the lists. We show that DL-Hom(H), parameterized by k and |H|, is fixed-parameter tractable for any (P6, C6)-free bipartite graph H; already for this restricted class of graphs, the problem generalizes Vertex Cover, Odd Cycle Transversal, and Vertex Multiway Cut parameterized by the size of the cutset and the number of terminals. We conjecture that DL-Hom(H) is fixed-parameter tractable for the class of graphs H for which the list homomorphism problem (without deletions) is polynomial-time solvable; by a result of Feder, Hell and Huang (1999), a graph H belongs to this class precisely if it is a bipartite graph whose complement is a circular arc graph. We show that this conjecture is equivalent to the fixed-parameter tractability of a single fairly natural satisfiability problem, Clause Deletion Chain-SAT.

cs.DS↗

arXiv2013

Immersions in highly edge connected graphs

We consider the problem of how much edge connectivity is necessary to force a graph G to contain a fixed graph H as an immersion. We show that if the maximum degree in H is D, then all the examples of D-edge connected graphs which do not contain H as a weak immersion must have a tree-like decomposition called a tree-cut decomposition of bounded width. If we consider strong immersions, then it is easy to see that there are arbitrarily highly edge connected graphs which do not contain a fixed clique K_t as a strong immersion. We give a structure theorem which roughly characterizes those highly edge connected graphs which do not contain K_t as a strong immersion.

math.CO↗

arXiv2011

On Problems as Hard as CNFSAT

The field of exact exponential time algorithms for NP-hard problems has thrived over the last decade. While exhaustive search remains asymptotically the fastest known algorithm for some basic problems, difficult and non-trivial exponential time algorithms have been found for a myriad of problems, including Graph Coloring, Hamiltonian Path, Dominating Set and 3-CNF-Sat. In some instances, improving these algorithms further seems to be out of reach. The CNF-Sat problem is the canonical example of a problem for which the trivial exhaustive search algorithm runs in time O(2^n), where n is the number of variables in the input formula. While there exist non-trivial algorithms for CNF-Sat that run in time o(2^n), no algorithm was able to improve the growth rate 2 to a smaller constant, and hence it is natural to conjecture that 2 is the optimal growth rate. The strong exponential time hypothesis (SETH) by Impagliazzo and Paturi [JCSS 2001] goes a little bit further and asserts that, for every epsilon<1, there is a (large) integer k such that that k-CNF-Sat cannot be computed in time 2^{epsilon n}. In this paper, we show that, for every epsilon < 1, the problems Hitting Set, Set Splitting, and NAE-Sat cannot be computed in time O(2^{epsilon n}) unless SETH fails. Here n is the number of elements or variables in the input. For these problems, we actually get an equivalence to SETH in a certain sense. We conjecture that SETH implies a similar statement for Set Cover, and prove that, under this assumption, the fastest known algorithms for Steinter Tree, Connected Vertex Cover, Set Partitioning, and the pseudo-polynomial time algorithm for Subset Sum cannot be significantly improved. Finally, we justify our assumption about the hardness of Set Cover by showing that the parity of the number of set covers cannot be computed in time O(2^{epsilon n}) for any epsilon<1 unless SETH fails.

cs.DS↗

arXiv2010

The complexity of global cardinality constraints

In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must be assigned a certain value. We study the complexity of the problem CCSP(G), the constraint satisfaction problem with global cardinality constraints that allows only relations from the set G. The main result of this paper characterizes sets G that give rise to problems solvable in polynomial time, and states that the remaining such problems are NP-complete.

cs.LO↗