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Minimum-cost paths for electric cars arXiv.cs.DS Pub Date : 2024-03-25 Dani Dorfman, Haim Kaplan, Robert E. Tarjan, Mikkel Thorup, Uri Zwick
An electric car equipped with a battery of a finite capacity travels on a road network with an infrastructure of charging stations. Each charging station has a possibly different cost per unit of energy. Traversing a given road segment requires a specified amount of energy that may be positive, zero or negative. The car can only traverse a road segment if it has enough charge to do so (the charge cannot
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A Novel exact algorithm for economic lot-sizing with piecewise linear production costs arXiv.cs.DS Pub Date : 2024-03-24 Kleitos Papadopoulos
In this paper, we study the single-item economic lot-sizing problem with production cost functions that are piecewise linear. The lot-sizing problem stands as a foundational cornerstone within the domain of lot-sizing problems. It is also applicable to a variety of important production planning problems which are special cases to it according to \cite{ou}. The problem becomes intractable when $m$,
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Hashing geographical point data using the space-filling H-curve arXiv.cs.DS Pub Date : 2024-03-24 Igor V. Netay
We construct geohashing procedure based on using of space-filling H-curve. This curve provides a way to construct geohash with less computations than the construction based on usage of Hilbert curve. At the same time, H-curve has better clustering properties.
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Convolution and Knapsack in Higher Dimensions arXiv.cs.DS Pub Date : 2024-03-24 Kilian Grage, Klaus Jansen
In the Knapsack problem, one is given the task of packing a knapsack of a given size with items in order to gain a packing with a high profit value. In recent years, a connection to the $(\max,+)$-convolution problem has been established, where knapsack solutions can be combined by building the convolution of two sequences. This observation has been used to give conditional lower bounds but also parameterized
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On the complexity and approximability of Bounded access Lempel Ziv coding arXiv.cs.DS Pub Date : 2024-03-23 Ferdinando Cicalese, Francesca Ugazio
We study the complexity of constructing an optimal parsing $\varphi$ of a string ${\bf s} = s_1 \dots s_n$ under the constraint that given a position $p$ in the original text, and the LZ76-like (Lempel Ziv 76) encoding of $T$ based on $\varphi$, it is possible to identify/decompress the character $s_p$ by performing at most $c$ accesses to the LZ encoding, for a given integer $c.$ We refer to such
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Distance Adjustment of a Graph Drawing Stress Model arXiv.cs.DS Pub Date : 2024-03-23 Yosuke Onoue
Stress models are a promising approach for graph drawing. They minimize the weighted sum of the squared errors of the Euclidean and desired distances for each node pair. The desired distance typically uses the graph-theoretic distances obtained from the all-node pair shortest path problem. In a minimized stress function, the obtained coordinates are affected by the non-Euclidean property and the high-dimensionality
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Approximation Algorithms for School Assignment: Group Fairness and Multi-criteria Optimization arXiv.cs.DS Pub Date : 2024-03-22 Santhini K. A., Kamesh Munagala, Meghana Nasre, Govind S. Sankar
We consider the problem of assigning students to schools, when students have different utilities for schools and schools have capacity. There are additional group fairness considerations over students that can be captured either by concave objectives, or additional constraints on the groups. We present approximation algorithms for this problem via convex program rounding that achieve various trade-offs
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Approximation Algorithms for Network Design in Non-Uniform Fault Models arXiv.cs.DS Pub Date : 2024-03-22 Chandra Chekuri, Rhea Jain
The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform fault models where the subset of edges that fail can be specified in different ways. Our primary interest is in the flexible graph connectivity model, in which the
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Maximum Polygon Packing: The CG:SHOP Challenge 2024 arXiv.cs.DS Pub Date : 2024-03-24 Sándor P. Fekete, Phillip Keldenich, Dominik Krupke, Stefan Schirra
We give an overview of the 2024 Computational Geometry Challenge targeting the problem \textsc{Maximum Polygon Packing}: Given a convex region $P$ in the plane, and a collection of simple polygons $Q_1, \ldots, Q_n$, each $Q_i$ with a respective value $c_i$, find a subset $S \subseteq \{1, \ldots,n\}$ and a feasible packing within $P$ of the polygons $Q_i$ (without rotation) for $i \in S$, maximizing
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Differentially Private Ad Conversion Measurement arXiv.cs.DS Pub Date : 2024-03-22 John Delaney, Badih Ghazi, Charlie Harrison, Christina Ilvento, Ravi Kumar, Pasin Manurangsi, Martin Pal, Karthik Prabhakar, Mariana Raykova
In this work, we study ad conversion measurement, a central functionality in digital advertising, where an advertiser seeks to estimate advertiser website (or mobile app) conversions attributed to ad impressions that users have interacted with on various publisher websites (or mobile apps). Using differential privacy (DP), a notion that has gained in popularity due to its strong mathematical guarantees
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Improved Algorithms for Maximum Coverage in Dynamic and Random Order Streams arXiv.cs.DS Pub Date : 2024-03-21 Amit Chakrabarti, Andrew McGregor, Anthony Wirth
The maximum coverage problem is to select $k$ sets from a collection of sets such that the cardinality of the union of the selected sets is maximized. We consider $(1-1/e-\epsilon)$-approximation algorithms for this NP-hard problem in three standard data stream models. 1. {\em Dynamic Model.} The stream consists of a sequence of sets being inserted and deleted. Our multi-pass algorithm uses $\epsilon^{-2}
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A simpler data structure for dynamic strings arXiv.cs.DS Pub Date : 2024-03-19 Zsuzsanna Lipták, Francesco Masillo, Gonzalo Navarro
We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem can be solved in optimal time $\mathcal{O}(\log N)$ whp for the updates and $\mathcal{O}(1)$ worst-case time for the queries, where $N$ is the total collection size
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Revisiting Local Computation of PageRank: Simple and Optimal arXiv.cs.DS Pub Date : 2024-03-19 Hanzhi Wang, Zhewei Wei, Ji-Rong Wen, Mingji Yang
We revisit the classic local graph exploration algorithm ApproxContributions proposed by Andersen, Borgs, Chayes, Hopcroft, Mirrokni, and Teng (WAW '07, Internet Math. '08) for computing an $\epsilon$-approximation of the PageRank contribution vector for a target node $t$ on a graph with $n$ nodes and $m$ edges. We give a worst-case complexity bound of ApproxContributions as $O(n\pi(t)/\epsilon\cdot\min(\Delta_{in}
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ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs arXiv.cs.DS Pub Date : 2024-03-18 Shinwoo An, Eunjin Oh
In this paper, we consider the Cycle Packing problem on unit disk graphs defined as follows. Given a unit disk graph G with n vertices and an integer k, the goal is to find a set of $k$ vertex-disjoint cycles of G if it exists. Our algorithm runs in time $2^{O(\sqrt k)}n^{O(1)}$. This improves the $2^{O(\sqrt k\log k)}n^{O(1)}$-time algorithm by Fomin et al. [SODA 2012, ICALP 2017]. Moreover, our algorithm
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A constant time complexity algorithm for the unbounded knapsack problem with bounded coefficients arXiv.cs.DS Pub Date : 2024-03-17 Yang Yang
Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range $R$, and these instances can be referred to as the unbounded knapsack problem with bounded coefficients (UKPB). In order to increase the difficulty of solving these instances, the knapsack capacity $C$ is usually set to a very large value. Therefore, an exact algorithm
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Approximation Ratio of the Min-Degree Greedy Algorithm for Maximum Independent Set on Interval and Chordal Graphs arXiv.cs.DS Pub Date : 2024-03-16 Steven Chaplick, Martin Frohn, Steven Kelk, Johann Lottermoser, Matus Mihalak
In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval graphs of maximum degree 3. We show that on chordal graphs, the greedy algorithm is a $(1/2)$-approximation and that this is again tight. These results contrast with
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First Passage Percolation with Queried Hints arXiv.cs.DS Pub Date : 2024-03-15 Kritkorn Karntikoon, Yiheng Shen, Sreenivas Gollapudi, Kostas Kollias, Aaron Schild, Ali Sinop
Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is noisy, uncertain, and expensive to obtain. In this work, we study how much of that information needs to be queried in order to obtain an approximately optimal solution
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Perfect Zero-Knowledge PCPs for #P arXiv.cs.DS Pub Date : 2024-03-18 Tom Gur, Jack O'Connor, Nicholas Spooner
We construct perfect zero-knowledge probabilistically checkable proofs (PZK-PCPs) for every language in #P. This is the first construction of a PZK-PCP for any language outside BPP. Furthermore, unlike previous constructions of (statistical) zero-knowledge PCPs, our construction simultaneously achieves non-adaptivity and zero knowledge against arbitrary (adaptive) polynomial-time malicious verifiers
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BAT-LZ Out of Hell arXiv.cs.DS Pub Date : 2024-03-14 Zsuzsanna Lipták, Francesco Masillo, Gonzalo Navarro
Despite consistently yielding the best compression on repetitive text collections, the Lempel-Ziv parsing has resisted all attempts at offering relevant guarantees on the cost to access an arbitrary symbol. This makes it less attractive for use on compressed self-indexes and other compressed data structures. In this paper we introduce a variant we call BAT-LZ (for Bounded Access Time Lempel-Ziv) where
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Lifted Causal Inference in Relational Domains arXiv.cs.DS Pub Date : 2024-03-15 Malte Luttermann, Mattis Hartwig, Tanya Braun, Ralf Möller, Marcel Gehrke
Lifted inference exploits symmetries in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. Even though lifting is a well-established technique for the task of probabilistic inference in relational domains, it has not yet been applied to the task of causal inference. In this paper, we show how lifting
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Efficient Detection of Exchangeable Factors in Factor Graphs arXiv.cs.DS Pub Date : 2024-03-15 Malte Luttermann, Johann Machemer, Marcel Gehrke
To allow for tractable probabilistic inference with respect to domain sizes, lifted probabilistic inference exploits symmetries in probabilistic graphical models. However, checking whether two factors encode equivalent semantics and hence are exchangeable is computationally expensive. In this paper, we efficiently solve the problem of detecting exchangeable factors in a factor graph. In particular
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Instance-optimal Clipping for Summation Problems in the Shuffle Model of Differential Privacy arXiv.cs.DS Pub Date : 2024-03-15 Wei Dong, Qiyao Luo, Giulia Fanti, Elaine Shi, Ke Yi
Differentially private mechanisms achieving worst-case optimal error bounds (e.g., the classical Laplace mechanism) are well-studied in the literature. However, when typical data are far from the worst case, \emph{instance-specific} error bounds -- which depend on the largest value in the dataset -- are more meaningful. For example, consider the sum estimation problem, where each user has an integer
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Efficient size-prescribed $k$-core search arXiv.cs.DS Pub Date : 2024-03-14 Yiping Liu, Bo Yan, Bo Zhao, Hongyi Su, Yang Chen, Michael Witbrock
$k$-core is a subgraph where every node has at least $k$ neighbors within the subgraph. The $k$-core subgraphs has been employed in large platforms like Network Repository to comprehend the underlying structures and dynamics of the network. Existing studies have primarily focused on finding $k$-core groups without considering their size, despite the relevance of solution sizes in many real-world scenarios
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Approximating Small Sparse Cuts arXiv.cs.DS Pub Date : 2024-03-13 Aditya Anand, Euiwoong Lee, Jason Li, Thatchaphol Saranurak
We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\, k)$-approximation algorithms for various versions in this setting. Our techniques involve an extension of the notion of sample sets (Feige and Mahdian STOC'06), originally
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Worst-Case to Expander-Case Reductions: Derandomized and Generalized arXiv.cs.DS Pub Date : 2024-03-13 Amir Abboud, Nathan Wallheimer
A recent paper by Abboud and Wallheimer [ITCS 2023] presents self-reductions for various fundamental graph problems, that transform worst-case instances to expanders, thus proving that the complexity remains unchanged if the input is assumed to be an expander. An interesting corollary of their self-reductions is that, if some problem admit such reduction, then the popular algorithmic paradigm based
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Height-bounded Lempel-Ziv encodings arXiv.cs.DS Pub Date : 2024-03-13 Hideo Bannai, Mitsuru Funakoshi, Diptarama Hendrian, Myuji Matsuda, Simon J. Puglisi
We introduce height-bounded LZ encodings (LZHB), a new family of compressed representations that is a variant of Lempel-Ziv parsings with a focus on allowing fast access to arbitrary positions of the text directly via the compressed representation. Any LZHB encoding whose referencing height is bounded by $h$ allows access to an arbitrary position of the underlying text using $O(h)$ predecessor queries
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Highway Preferential Attachment Models for Geographic Routing arXiv.cs.DS Pub Date : 2024-03-12 Ofek GilaUniversity of California, Irvine, Evrim OzelUniversity of California, Irvine, Michael T. GoodrichUniversity of California, Irvine
In the 1960s, the world-renowned social psychologist Stanley Milgram conducted experiments that showed that not only do there exist ``short chains'' of acquaintances between any two arbitrary people, but that these arbitrary strangers are able to find these short chains. This phenomenon, known as the \emph{small-world phenomenon}, is explained in part by any model that has a low diameter, such as the
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Simplified Tight Bounds for Monotone Minimal Perfect Hashing arXiv.cs.DS Pub Date : 2024-03-12 Dmitry Kosolobov
Given an increasing sequence of integers $x_1,\ldots,x_n$ from a universe $\{0,\ldots,u-1\}$, the monotone minimal perfect hash function (MMPHF) for this sequence is a data structure that answers the following rank queries: $rank(x) = i$ if $x = x_i$, for $i\in \{1,\ldots,n\}$, and $rank(x)$ is arbitrary otherwise. Assadi, Farach-Colton, and Kuszmaul recently presented at SODA'23 a proof of the lower
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Shining Light on Periodic Dominating Sets in Bounded-Treewidth Graphs arXiv.cs.DS Pub Date : 2024-03-12 Jakob Greilhuber, Philipp Schepper, Philip Wellnitz
For the vertex selection problem $(\sigma,\rho)$-DomSet one is given two fixed sets $\sigma$ and $\rho$ of integers and the task is to decide whether we can select vertices of the input graph, such that, for every selected vertex, the number of selected neighbors is in $\sigma$ and, for every unselected vertex, the number of selected neighbors is in $\rho$. This framework covers Independent Set and
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Satisfiability to Coverage in Presence of Fairness, Matroid, and Global Constraints arXiv.cs.DS Pub Date : 2024-03-12 Tanmay Inamdar, Pallavi Jain, Daniel Lokshtanov, Abhishek Sahu, Saket Saurabh, Anannya Upasana
In MaxSAT with Cardinality Constraint problem (CC-MaxSAT), we are given a CNF-formula $\Phi$, and $k \ge 0$, and the goal is to find an assignment $\beta$ with at most $k$ variables set to true (also called a weight $k$-assignment) such that the number of clauses satisfied by $\beta$ is maximized. MaxCov can be seen as a special case of CC-MaxSAT, where the formula $\Phi$ is monotone, i.e., does not
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Noisy Computing of the Threshold Function arXiv.cs.DS Pub Date : 2024-03-12 Ziao Wang, Nadim Ghaddar, Banghua Zhu, Lele Wang
Let $\mathsf{TH}_k$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}_k$ function using noisy readings of the Boolean variables, where each reading is incorrect with some fixed and known probability $p \in (0,1/2)$. As our main result, we show that
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Controlling Delegations in Liquid Democracy arXiv.cs.DS Pub Date : 2024-03-12 Shiri Alouf-Heffetz, Tanmay Inamdar, Pallavi Jain, Yash More, Nimrod Talmon
In liquid democracy, agents can either vote directly or delegate their vote to a different agent of their choice. This results in a power structure in which certain agents possess more voting weight than others. As a result, it opens up certain possibilities of vote manipulation, including control and bribery, that do not exist in standard voting scenarios of direct democracy. Here we formalize a certain
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The Primal Pathwidth SETH arXiv.cs.DS Pub Date : 2024-03-12 Michael Lampis
Motivated by the importance of dynamic programming (DP) in parameterized complexity, we consider several fine-grained questions, such as the following examples: (i) can Dominating Set be solved in time $(3-\epsilon)^{pw}n^{O(1)}$? (where $pw$ is the pathwidth) (ii) can Coloring be solved in time $pw^{(1-\epsilon)pw}n^{O(1)}$? (iii) can a short reconfiguration between two size-$k$ independent sets be
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Balanced Substructures in Bicolored Graphs arXiv.cs.DS Pub Date : 2024-03-11 P. S. Ardra, R. Krithika, Saket Saurabh, Roohani Sharma
An edge-colored graph is said to be balanced if it has an equal number of edges of each color. Given a graph $G$ whose edges are colored using two colors and a positive integer $k$, the objective in the Edge Balanced Connected Subgraph problem is to determine if $G$ has a balanced connected subgraph containing at least $k$ edges. We first show that this problem is NP-complete and remains so even if
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Fun Maximizing Search, (Non) Instance Optimality, and Video Games for Parrots arXiv.cs.DS Pub Date : 2024-03-11 Jérémy Barbay
Computerized Adaptive Testing (CAT) measures an examinee's ability while adapting to their level. Both too many questions and too many hard questions can make a test frustrating. Are there some CAT algorithms which can be proven to be theoretically better than others, and in which framework? We show that slightly extending the traditional framework yields a partial order on CAT algorithms. For uni-dimensional
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Improved FPT Approximation Scheme and Approximate Kernel for Biclique-Free Max k-Weight SAT: Greedy Strikes Back arXiv.cs.DS Pub Date : 2024-03-10 Pasin Manurangsi
In the Max $k$-Weight SAT (aka Max SAT with Cardinality Constraint) problem, we are given a CNF formula with $n$ variables and $m$ clauses together with a positive integer $k$. The goal is to find an assignment where at most $k$ variables are set to one that satisfies as many constraints as possible. Recently, Jain et al. [SODA'23] gave an FPT approximation scheme (FPT-AS) with running time $2^{O\
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Revisiting Path Contraction and Cycle Contraction arXiv.cs.DS Pub Date : 2024-03-10 R. Krithika, V. K. Kutty Malu, Prafullkumar Tale
The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge contractions in $G$. We revisit these NP-complete problems and prove the following results. Path Contraction admits an algorithm running in $\mathcal{O}^*(2^{k})$
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Approximate Bipartite $b$-Matching using Multiplicative Auction arXiv.cs.DS Pub Date : 2024-03-09 Bhargav Samineni, S M Ferdous, Mahantesh Halappanavar, Bala Krishnamoorthy
Given a bipartite graph $G(V= (A \cup B),E)$ with $n$ vertices and $m$ edges and a function $b \colon V \to \mathbb{Z}_+$, a $b$-matching is a subset of edges such that every vertex $v \in V$ is incident to at most $b(v)$ edges in the subset. When we are also given edge weights, the Max Weight $b$-Matching problem is to find a $b$-matching of maximum weight, which is a fundamental combinatorial optimization
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Scalable $k$-clique Densest Subgraph Search arXiv.cs.DS Pub Date : 2024-03-09 Xiaowei Ye, Miao Qiao, Rong-Hua Li, Qi Zhang, Guoren Wang
In this paper, we present a collection of novel and scalable algorithms designed to tackle the challenges inherent in the $k$-clique densest subgraph problem (\kcdsp) within network analysis. We propose \psctl, a novel algorithm based on the Frank-Wolfe approach for addressing \kcdsp, effectively solving a distinct convex programming problem. \textcolor{black}{\psctl is able to approximate \kcdsp with
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An Algorithm for Correct Computation of Reeb Spaces for PL Bivariate Fields arXiv.cs.DS Pub Date : 2024-03-11 Amit Chattopadhyay, Yashwanth Ramamurthi, Osamu Saeki
The Reeb space is a topological structure which is a generalization of the notion of the Reeb graph to multi-fields. Its effectiveness has been established in revealing topological features in data across diverse computational domains which cannot be identified using the Reeb graph or other scalar-topology-based methods. Approximations of Reeb spaces such as the Mapper and the Joint Contour Net have
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Dynamic Convex Hulls for Simple Paths arXiv.cs.DS Pub Date : 2024-03-08 Bruce Brewer, Gerth Stølting Brodal, Haitao Wang
We consider the planar dynamic convex hull problem. In the literature, solutions exist supporting the insertion and deletion of points in poly-logarithmic time and various queries on the convex hull of the current set of points in logarithmic time. If arbitrary insertion and deletion of points are allowed, constant time updates and fast queries are known to be impossible. This paper considers two restricted
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Efficient Algorithms for Personalized PageRank Computation: A Survey arXiv.cs.DS Pub Date : 2024-03-08 Mingji Yang, Hanzhi Wang, Zhewei Wei, Sibo Wang, Ji-Rong Wen
Personalized PageRank (PPR) is a traditional measure for node proximity on large graphs. For a pair of nodes $s$ and $t$, the PPR value $\pi_s(t)$ equals the probability that an $\alpha$-discounted random walk from $s$ terminates at $t$ and reflects the importance between $s$ and $t$ in a bidirectional way. As a generalization of Google's celebrated PageRank centrality, PPR has been extensively studied
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Single Family Algebra Operation on ZDDs Leads To Exponential Blow-Up arXiv.cs.DS Pub Date : 2024-03-08 Kengo Nakamura, Masaaki Nishino, Shuhei Denzumi
Zero-suppressed binary decision diagram (ZDD) is a data structure to represent a family of (sub)sets compactly, and it can be used as a succinct index for a family of sets. To build ZDD representing a desired family of sets, there are many transformation operations that take ZDDs as inputs and output ZDD representing the resultant family after performing operations such as set union and intersection
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Data-Dependent LSH for the Earth Mover's Distance arXiv.cs.DS Pub Date : 2024-03-08 Rajesh Jayaram, Erik Waingarten, Tian Zhang
We give new data-dependent locality sensitive hashing schemes (LSH) for the Earth Mover's Distance ($\mathsf{EMD}$), and as a result, improve the best approximation for nearest neighbor search under $\mathsf{EMD}$ by a quadratic factor. Here, the metric $\mathsf{EMD}_s(\mathbb{R}^d,\ell_p)$ consists of sets of $s$ vectors in $\mathbb{R}^d$, and for any two sets $x,y$ of $s$ vectors the distance $\mathsf{EMD}(x
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A basic lower bound for property testing arXiv.cs.DS Pub Date : 2024-03-08 Eldar Fischer
An $\epsilon$-test for any non-trivial property (one for which there are both satisfying inputs and inputs of large distance from the property) should use a number of queries that is at least inversely proportional in $\epsilon$. However, to the best of our knowledge there is no reference proof for this intuition. Such a proof is provided here. It is written so as to not require any prior knowledge
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NP-Completeness for the Space-Optimality of Double-Array Tries arXiv.cs.DS Pub Date : 2024-03-07 Hideo Bannai, Keisuke Goto, Shunsuke Kanda, Dominik Köppl
Indexing a set of strings for prefix search or membership queries is a fundamental task with many applications such as information retrieval or database systems. A classic abstract data type for modelling such an index is a trie. Due to the fundamental nature of this problem, it has sparked much interest, leading to a variety of trie implementations with different characteristics. A trie implementation
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Improved Lower Bound for Differentially Private Facility Location arXiv.cs.DS Pub Date : 2024-03-07 Pasin Manurangsi
We consider the differentially private (DP) facility location problem in the so called super-set output setting proposed by Gupta et al. [SODA 2010]. The current best known expected approximation ratio for an $\epsilon$-DP algorithm is $O\left(\frac{\log n}{\sqrt{\epsilon}}\right)$ due to Cohen-Addad et al. [AISTATS 2022] where $n$ denote the size of the metric space, meanwhile the best known lower
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Time-Aware Projections: Truly Node-Private Graph Statistics under Continual Observation arXiv.cs.DS Pub Date : 2024-03-07 Palak Jain, Adam Smith, Connor Wagaman
We describe the first algorithms that satisfy the standard notion of node-differential privacy in the continual release setting (i.e., without an assumed promise on input streams). Previous work addresses node-private continual release by assuming an unenforced promise on the maximum degree in a graph; indeed, the algorithms from these works exhibit blatant privacy violations when the degree bound
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Optimizing Inventory Placement for a Downstream Online Matching Problem arXiv.cs.DS Pub Date : 2024-03-07 Boris EpsteinColumbia University, Will MaColumbia University
We study the inventory placement problem of splitting $Q$ units of a single item across warehouses, in advance of a downstream online matching problem that represents the dynamic fulfillment decisions of an e-commerce retailer. This is a challenging problem both in theory, because the downstream matching problem itself is computationally hard, and in practice, because the fulfillment team is constantly
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A Simple and Near-Optimal Algorithm for Directed Expander Decompositions arXiv.cs.DS Pub Date : 2024-03-07 Aurelio L. Sulser, Maximilian Probst Gutenberg
In this work, we present the first algorithm to compute expander decompositions in an $m$-edge directed graph with near-optimal time $\tilde{O}(m)$. Further, our algorithm can maintain such a decomposition in a dynamic graph and again obtains near-optimal update times. Our result improves over previous algorithms of Bernstein-Probst Gutenberg-Saranurak (FOCS 2020), Hua-Kyng-Probst Gutenberg-Wu (SODA
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Equivalence Testing: The Power of Bounded Adaptivity arXiv.cs.DS Pub Date : 2024-03-07 Diptarka Chakraborty, Sourav Chakraborty, Gunjan Kumar, Kuldeep S. Meel
Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful query model and has been investigated by theoreticians and practitioners alike, leading to the design of optimal algorithms albeit in a sequential setting (also
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A Sierpinski Triangle Data Structure for Efficient Array Value Update and Prefix Sum Calculation arXiv.cs.DS Pub Date : 2024-03-06 Brent Harrison, Jason Necaise, Andrew Projansky, James D. Whitfield
The binary indexed tree, or Fenwick tree, is a data structure that can efficiently update values and calculate prefix sums in an array. It allows both of these operations to be performed in $O(\log_2 N)$ time. Here we present a novel data structure resembling the Sierpinski triangle, which accomplishes these operations with the same memory usage in $O(\log_3 N)$ time instead. We show this order to
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Conflict and Fairness in Resource Allocation arXiv.cs.DS Pub Date : 2024-03-07 Susobhan Bandopadhyay, Aritra Banik, Sushmita Gupta, Pallavi Jain, Abhishek Sahu, Saket Saurabh, Prafullkumar Tale
In the standard model of fair allocation of resources to agents, every agent has some utility for every resource, and the goal is to assign resources to agents so that the agents' welfare is maximized. Motivated by job scheduling, interest in this problem dates back to the work of Deuermeyer et al. [SIAM J. on Algebraic Discrete Methods'82]. Recent works consider the compatibility between resources
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On HTLC-Based Protocols for Multi-Party Cross-Chain Swaps arXiv.cs.DS Pub Date : 2024-03-06 Emily Clark, Chloe Georgiou, Katelyn Poon, Marek Chrobak
In his 2018 paper, Herlihy introduced an atomic protocol for multi-party asset swaps across different blockchains. His model represents an asset swap by a directed graph whose nodes are the participating parties and edges represent asset transfers, and rational behavior of the participants is captured by a preference relation between a protocol's outcomes. Asset transfers between parties are achieved
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Double Exponential Lower Bound for Telephone Broadcast arXiv.cs.DS Pub Date : 2024-03-06 Prafullkumar Tale
Consider the Telephone Broadcast problem in which an input is a connected graph $G$ on $n$ vertices, a source vertex $s \in V(G)$, and a positive integer $t$. The objective is to decide whether there is a broadcast protocol from $s$ that ensures that all the vertices of $G$ get the message in at most $t$ rounds. We consider the broadcast protocol where, in a round, any node aware of the message can
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Fine-Grained Privacy Guarantees for Coverage Problems arXiv.cs.DS Pub Date : 2024-03-05 Laxman Dhulipala, George Z. Li
We introduce a new notion of neighboring databases for coverage problems such as Max Cover and Set Cover under differential privacy. In contrast to the standard privacy notion for these problems, which is analogous to node-privacy in graphs, our new definition gives a more fine-grained privacy guarantee, which is analogous to edge-privacy. We illustrate several scenarios of Set Cover and Max Cover
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Maintaining Light Spanners via Minimal Updates arXiv.cs.DS Pub Date : 2024-03-05 Hadi Khodabandeh, David Eppstein
We study the problem of maintaining a lightweight bounded-degree $(1+\varepsilon)$-spanner of a dynamic point set in a $d$-dimensional Euclidean space, where $\varepsilon>0$ and $d$ are arbitrary constants. In our fully-dynamic setting, points are allowed to be inserted as well as deleted, and our objective is to maintain a $(1+\varepsilon)$-spanner that has constant bounds on its maximum degree and
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The Exchange Problem arXiv.cs.DS Pub Date : 2024-03-05 Mohit Garg, Suneel Sarswat
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the matching are maximizing volume at a uniform price and maximizing volume with dynamic pricing. In this work, we study the algorithmic complexity of the problems
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Cover Edge-Based Novel Triangle Counting arXiv.cs.DS Pub Date : 2024-03-05 David A. Bader, Fuhuan Li, Zhihui Du, Palina Pauliuchenka, Oliver Alvarado Rodriguez, Anant Gupta, Sai Sri Vastav Minnal, Valmik Nahata, Anya Ganeshan, Ahmet Gundogdu, Jason Lew
Listing and counting triangles in graphs is a key algorithmic kernel for network analyses, including community detection, clustering coefficients, k-trusses, and triangle centrality. In this paper, we propose the novel concept of a cover-edge set that can be used to find triangles more efficiently. Leveraging the breadth-first search (BFS) method, we can quickly generate a compact cover-edge set. Novel
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Algorithms for Galois Words: Detection, Factorization, and Rotation arXiv.cs.DS Pub Date : 2024-03-05 Diptarama Hendrian, Dominik Köppl, Ryo Yoshinaka, Ayumi Shinohara
Lyndon words are extensively studied in combinatorics on words -- they play a crucial role on upper bounding the number of runs a word can have [Bannai+, SIAM J. Comput.'17]. We can determine Lyndon words, factorize a word into Lyndon words in lexicographically decreasing order, and find the Lyndon rotation of a word, all in linear time within constant additional working space. A recent research interest