5,518 Works

Faster Algorithms for Half-Integral T-Path Packing

Maxim Babenko & Stepan Artamonov
Let G = (V, E) be an undirected graph, a subset of vertices T be a set of terminals. Then a natural combinatorial problem consists in finding the maximum number of vertex-disjoint paths connecting distinct terminals. For this problem, a clever construction suggested by Gallai reduces it to computing a maximum non-bipartite matching and thus gives an O(mn^1/2 log(n^2/m)/log(n))-time algorithm (hereinafter n := |V|, m := |E|). Now let us consider the fractional relaxation, i.e....

Computational Philosophy: On Fairness in Automated Decision Making

Suresh Venkatasubramanian
As more and more of our lives are taken over by automated decision making systems (whether it be for hiring, college admissions, criminal justice or loans), we have begun to ask whether these systems are making decisions that humans would consider fair, or non-discriminatory. The problem is that notions of fairness, discrimination, transparency and accountability are concepts in society and the law that have no obvious formal analog. But our algorithms speak the language of...

Agnostically Learning Boolean Functions with Finite Polynomial Representation

Ning Ding
Agnostic learning is an extremely hard task in computational learning theory. In this paper we revisit the results in [Kalai et al. SIAM J. Comput. 2008] on agnostically learning boolean functions with finite polynomial representation and those that can be approximated by the former. An example of the former is the class of all boolean low-degree polynomials. For the former, [Kalai et al. SIAM J. Comput. 2008] introduces the l_1-polynomial regression method to learn them...

Weighted Linear Matroid Parity

Satoru Iwata
The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lovasz (1978) showed that this problem admits a min-max formula and a polynomial algorithm for linearly represented matroids. Since then efficient algorithms have been developed for the linear matroid parity problem. This talk presents a recently developed polynomial-time algorithm for the weighted linear matroid...

Optimal Matroid Partitioning Problems

Yasushi Kawase, Kei Kimura, Kazuhisa Makino & Hanna Sumita
This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set E and k weighted matroids (E, \mathcal{I}_i, w_i), i = 1, \dots, k, and our task is to find a minimum partition (I_1,\dots,I_k) of E such that I_i \in \mathcal{I}_i for all i. For each objective function, we give a polynomial-time algorithm or prove NP-hardness. In particular, for the case when the given weighted matroids...

Network Optimization on Partitioned Pairs of Points

Esther M. Arkin, Aritra Banik, Paz Carmi, Gui Citovsky, Su Jia, Matthew J Katz, Tyler Mayer & Joseph S. B. Mitchell
Given n pairs of points, S = {{p_1, q_1}, {p_2, q_2}, ..., {p_n, q_n}}, in some metric space, we study the problem of two-coloring the points within each pair, red and blue, to optimize the cost of a pair of node-disjoint networks, one over the red points and one over the blue points. In this paper we consider our network structures to be spanning trees, traveling salesman tours or matchings. We consider several different weight...

Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points

Mark De Berg, Tim Leijsen, Aleksandar Markovic, André Van Renssen, Marcel Roeloffzen & Gerhard Woeginger
We introduce the fully-dynamic conflict-free coloring problem for a set S of intervals in R^1 with respect to points, where the goal is to maintain a conflict-free coloring for S under insertions and deletions. A coloring is conflict-free if for each point p contained in some interval, p is contained in an interval whose color is not shared with any other interval containing p. We investigate trade-offs between the number of colors used and the...

Tight Approximation for Partial Vertex Cover with Hard Capacities

Jia-Yau Shiau, Mong-Jen Kao, Ching-Chi Lin & D.T. Lee
We consider the partial vertex cover problem with hard capacity constraints (Partial VC-HC) on hypergraphs. In this problem we are given a hypergraph G=(V,E) with a maximum edge size f and a covering requirement R. Each edge is associated with a demand, and each vertex is associated with a capacity and an (integral) available multiplicity. The objective is to compute a minimum vertex multiset such that at least R units of demand from the edges...

Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs

Giordano Da Lozzo, William E. Devanny, David Eppstein & Timothy Johnson
A square-contact representation of a planar graph G = (V,E) maps vertices in V to interior-disjoint axis-aligned squares in the plane and edges in E to adjacencies between the sides of the corresponding squares. In this paper, we study proper square-contact representations of planar graphs, in which any two squares are either disjoint or share infinitely many points. We characterize the partial 2-trees and the triconnected cycle-trees allowing for such representations. For partial 2-trees our...

An Improved Algorithm for Computing All the Best Swap Edges of a Tree Spanner

Davide Bilò, Feliciano Colella, Luciano Gualà, Stefano Leucci & Guido Proietti
A tree sigma-spanner of a positively real-weighted n-vertex and m-edge undirected graph G is a spanning tree T of G which approximately preserves (i.e., up to a multiplicative stretch factor sigma) distances in G. Tree spanners with provably good stretch factors find applications in communication networks, distributed systems, and network design. However, finding an optimal or even a good tree spanner is a very hard computational task. Thus, if one has to face a transient...

Precedence-Constrained Min Sum Set Cover

Jessica McClintock, Julián Mestre & Anthony Wirth
We introduce a version of the Min Sum Set Cover (MSSC) problem in which there are "AND" precedence constraints on the m sets. In the Precedence-Constrained Min Sum Set Cover (PCMSSC) problem, when interpreted as directed edges, the constraints induce an acyclic directed graph. PCMSSC models the aim of scheduling software tests to prioritize the rate of fault detection subject to dependencies between tests. Our greedy scheme for PCMSSC is similar to the approaches of...

Sorting with Recurrent Comparison Errors

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu & Paolo Penna
We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting n distinct elements in this model. In particular, it runs in O(n^2) time, the maximum dislocation of the elements in the output is O(log n), while the total dislocation is O(n). These guarantees are the best possible since we prove that even randomized algorithms cannot achieve o(log n) maximum dislocation...

A Simple Greedy Algorithm for Dynamic Graph Orientation

Edvin Berglin & Gerth Stølting Brodal
Graph orientations with low out-degree are one of several ways to efficiently store sparse graphs. If the graphs allow for insertion and deletion of edges, one may have to flip the orientation of some edges to prevent blowing up the maximum out-degree. We use arboricity as our sparsity measure. With an immensely simple greedy algorithm, we get parametrized trade-off bounds between out-degree and worst case number of flips, which previously only existed for amortized number...

Decomposing a Graph into Shortest Paths with Bounded Eccentricity

Etienne Birmelé, Fabien De Montgolfier, Léo Planche & Laurent Viennot
We introduce the problem of hub-laminar decomposition which generalizes that of computing a shortest path with minimum eccentricity (MESP). Intuitively, it consists in decomposing a graph into several paths that collectively have small eccentricity and meet only near their extremities. The problem is related to computing an isometric cycle with minimum eccentricity (MEIC). It is also linked to DNA reconstitution in the context of metagenomics in biology. We show that a graph having such a...

Fully Dynamic Connectivity Oracles under General Vertex Updates

Kengo Nakamura
We study the following dynamic graph problem: given an undirected graph G, we maintain a connectivity oracle between any two vertices in G under any on-line sequence of vertex deletions and insertions with incident edges. We propose two algorithms for this problem: an amortized update time deterministic one and a worst case update time Monte Carlo one. Both of them allow an arbitrary number of new vertices to insert. The update time complexity of the...

Almost Linear Time Computation of Maximal Repetitions in Run Length Encoded Strings

Yuta Fujishige, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai & Masayuki Takeda
We consider the problem of computing all maximal repetitions contained in a string that is given in run-length encoding. Given a run-length encoding of a string, we show that the maximum number of maximal repetitions contained in the string is at most m+k-1, where m is the size of the run-length encoding, and k is the number of run-length factors whose exponent is at least 2. We also show an algorithm for computing all maximal...

Barrier Coverage with Non-uniform Lengths to Minimize Aggregate Movements

Serge Gaspers, Joachim Gudmundsson, Julián Mestre & Stefan Rümmele
Given a line segment I=[0,L], the so-called barrier, and a set of n sensors with varying ranges positioned on the line containing I, the barrier coverage problem is to move the sensors so that they cover I, while minimising the total movement. In the case when all the sensors have the same radius the problem can be solved in O(n log n) time (Andrews and Wang, Algorithmica 2017). If the sensors have different radii the...

Crossing Number for Graphs with Bounded~Pathwidth

Therese Biedl, Markus Chimani, Martin Derka & Petra Mutzel
The crossing number is the smallest number of pairwise edge crossings when drawing a graph into the plane. There are only very few graph classes for which the exact crossing number is known or for which there at least exist constant approximation ratios. Furthermore, up to now, general crossing number computations have never been successfully tackled using bounded width of graph decompositions, like treewidth or pathwidth. In this paper, we for the first time show...

Complexity of Coloring Reconfiguration under Recolorability Constraints

Hiroki Osawa, Akira Suzuki, Takehiro Ito & Xiao Zhou
For an integer k \ge 1, k-coloring reconfiguration is one of the most well-studied reconfiguration problems, defined as follows: In the problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper coloring. The problem is known to be PSPACE-complete if k \ge 4, and solvable for any graph in polynomial...

Structural Pattern Matching - Succinctly

Arnab Ganguly, Rahul Shah & Sharma V. Thankachan
Let T be a text of length n containing characters from an alphabet \Sigma, which is the union of two disjoint sets: \Sigma_s containing static characters (s-characters) and \Sigma_p containing parameterized characters (p-characters). Each character in \Sigma_p has an associated complementary character from \Sigma_p. A pattern P (also over \Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a one-to-one function that renames the p-characters in S to the...

On Structural Parameterizations of the Edge Disjoint Paths Problem

Robert Ganian, Sebastian Ordyniak & Ramanujan Sridharan
In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our focus lies on structural parameterizations for the problem that allow for efficient (polynomial-time or fpt) algorithms. As our first result, we answer an open question stated in Fleszar, Mnich, and...

Complexity of the Multi-Service Center Problem

Takehiro Ito, Naonori Kakimura & Yusuke Kobayashi
The multi-service center problem is a variant of facility location problems. In the problem, we consider locating p facilities on a graph, each of which provides distinct service required by all vertices. Each vertex incurs the cost determined by the sum of the weighted distances to the p facilities. The aim of the problem is to minimize the maximum cost among all vertices. This problem is known to be NP-hard for general graphs, while it...

On Using Toeplitz and Circulant Matrices for Johnson-Lindenstrauss Transforms

Casper Benjamin Freksen & Kasper Green Larsen
The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that given N, for any set of N, vectors X \subset R^n, there exists a mapping f : X --> R^m such that f(X) preserves all pairwise distances between vectors in X to within(1 ± \eps) if m = O(\eps^{-2} lg N). Much effort has gone into developing fast embedding algorithms, with the Fast Johnson-Lindenstrauss transform of Ailon and Chazelle...

On-the-Fly Array Initialization in Less Space

Torben Hagerup & Frank Kammer
We show that for all given n,t,w in {1,2,...} with n<2^w, an array of n entries of w bits each can be represented on a word RAM with a word length of w bits in at most nw+ceil(n(t/(2 w))^t) bits of uninitialized memory to support constant-time initialization of the whole array and O(t)-time reading and writing of individual array entries. At one end of this tradeoff, we achieve initialization and access (i.e., reading and writing)...

Temporal Hierarchical Clustering

Tamal K. Dey, Alfred Rossi & Anastasios Sidiropoulos
We study hierarchical clusterings of metric spaces that change over time. This is a natural geo- metric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent sequence of hierarchical clusterings from a sequence of unlabeled point sets. We encode the clustering objective by embedding each point set into an ultrametric space, which naturally induces a hierarchical clustering of the set of points. We enforce...

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