This paper addresses the classic online Steiner tree problem on edge-weighted graphs. It is known that a greedy (nearest neighbor) online algorithm has a tight competitive ratio for wide classes of graphs, such as trees, rings, any class including series-parallel graphs, and unweighted graphs with bounded diameter. However, we do not know any greedy or non-greedy tight deterministic algorithm for other

We consider the inverse Voronoi diagram problem in trees: given a tree T with positive edge-lengths and a collection \(\mathbb {U}\) of subsets of vertices of V(T), decide whether \({\mathbb {U}}\) is a Voronoi diagram in T with respect to the shortest-path metric. We show that the problem can be solved in \(O(N+n \log ^2 n)\) time, where n is the number of vertices in T and \(N=n+\sum _{U\in {\mathbb

Agrawal et al. (ACM Trans Comput Theory 10(4):18:1–18:25, 2018. https://doi.org/10.1145/3265027) studied a simultaneous variant of the classic Feedback Vertex Set problem, called Simultaneous Feedback Vertex Set (Sim-FVS). Here, we consider the edge variant of the problem, namely, Simultaneous Feedback Edge Set (Sim-FES). In this problem, the input is an n-vertex graph G, a positive integer k, and

We study the two party problem of randomly selecting a common string among all the strings of length n. We want the protocol to have the property that the output distribution has high Shannon entropy or high min entropy, even when one of the two parties is dishonest and deviates from the protocol. We develop protocols that achieve high, close to n, Shannon entropy and simultaneously min entropy close

Obvious strategyproofness (OSP) is an appealing concept as it allows to maintain incentive compatibility even in the presence of agents that are not fully rational, i.e., those who struggle with contingent reasoning (Li in Am Econ Rev 107(11):3257–3287, 2017). However, it has been shown to impose some limitations, e.g., no OSP mechanism can return a stable matching (Ashlagi and Gonczarowski in J Econ

In this article, we study some fault-tolerant covering problems in metric spaces. In the metric multi-cover problem (MMC), we are given two point sets Y (servers) and X (clients) in an arbitrary metric space \((X \cup Y, d)\), a positive integer k that represents the coverage demand of each client, and a constant \(\alpha \ge 1\). Each server can host a single ball of arbitrary radius centered on it

There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see within a rectangle, along a staircase, or along an orthogonal path with at most k bends. In this paper, we study all these guarding models for the special case of orthogonal polygons that have bounded treewidth in some sense. As our main result, we show that the problem of finding the minimum

We revisit the complexity of deciding, given a bimatrix game, whether it has a Nash equilibrium with certain natural properties; such decision problems were early known to be \({{\mathcal{N}}{\mathcal{P}}}\)-hard (Gilboa and Zemel in Games Econ Behav 1(1):80–93, 1989). We show that \({{\mathcal{N}}{\mathcal{P}}}\)-hardness still holds under two significant restrictions in simultaneity: the game is

Let \(G\) be a random geometric graph formed by \(n\) nodes with adjacency distance \(r_n\) and let each edge of \(G\) be assigned an independent exponential passage time with mean that depends on the graph size \(n.\) We connect \(G\) to two nodes source \(s_A\) and destination \(s_B\) at deterministic locations spaced \(d_n\) apart in the unit square and find upper and lower bounds on the minimum

A graph G is prismatic if for every triangle T of G, every vertex of G not in T has a unique neighbour in T. The complement of a prismatic graph is called antiprismatic. The complexity of colouring antiprismatic graphs is still unknown. Equivalently, the complexity of the clique cover problem in prismatic graphs is not known. Chudnovsky and Seymour gave a full structural description of prismatic graphs

In the Tree Augmentation problem we are given a tree \(T=(V,F)\) and a set \(E \subseteq V \times V\) of edges with positive integer costs \(\{c_e:e \in E\}\). The goal is to augment T by a minimum cost edge set \(J \subseteq E\) such that \(T \cup J\) is 2-edge-connected. We obtain the following results. Recently, Adjiashvili [SODA 17] introduced a novel LP for the problem and used it to break the

Distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the distance between any two vertices u and v can be determined efficiently by merely inspecting the labels of u and v, without using any other information. Similarly, routing labeling schemes label the vertices of a graph in a such a way that given the labels of a source node and a destination

We contribute results for a set of fundamental problems in the context of programmable matter by presenting algorithmic methods for evaluating and manipulating a collective of particles by a finite automaton that can neither store significant amounts of data, nor perform complex computations, and is limited to a handful of possible physical operations. We provide a toolbox for carrying out fundamental

Low-treedepth colorings are an important tool for algorithms that exploit structure in classes of bounded expansion; they guarantee subgraphs that use few colors have bounded treedepth. These colorings have an implicit tradeoff between the total number of colors used and the treedepth bound, and prior empirical work suggests that the former dominates the run time of existing algorithms in practice

Traditionally, computation within self-assembly models is hard to conceal because the self-assembly process generates a crystalline assembly whose computational history is inherently part of the structure itself. With no way to remove information from the computation, this computational model offers a unique problem: how can computational input and computation be hidden while still computing and reporting

We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our bounds also hold for randomized online algorithms, for which hardly any results were known. Technically, we construct lower bounds for chordal graphs. The constructions

We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound. Our focus lies on parameters that measure the structural properties of the input instance. We first show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters

We consider the problem of maximizing the sum of a monotone submodular function and a linear function subject to a general solvable polytope constraint. Recently, Sviridenko et al. (Math Oper Res 42(4):1197–1218, 2017) described an algorithm for this problem whose approximation guarantee is optimal in some intuitive and formal senses. Unfortunately, this algorithm involves a guessing step which makes

We resolve the computational complexity of Graph Isomorphism for classes of graphs characterized by two forbidden induced subgraphs \( H_{1} \) and \(H_2\) for all but six pairs \((H_1,H_2)\). Schweitzer had previously shown that the number of open cases was finite, but without specifying the open cases. Grohe and Schweitzer proved that Graph Isomorphism is polynomial-time solvable on graph classes

We provide a simple and novel algorithmic design technique, for which we call iterative partial rounding, that gives a tight rounding-based approximation for vertex cover with hard capacities (VC-HC). In particular, we obtain an f-approximation for VC-HC on hypergraphs, improving over a previous results of Cheung et al. (In: SODA’14, 2014) to the tight extent. This also closes the gap of approximation

We study the problem of enumerating the k-arc-connected orientations of a graph G, i.e., generating each exactly once. A first algorithm using submodular flow optimization is easy to state, but intricate to implement. In a second approach we present a simple algorithm with \(O(knm^2)\) time delay and amortized time \(O(m^2)\), which improves over the analysis of the submodular flow algorithm. As ingredients

A private learner is an algorithm that given a sample of labeled individual examples outputs a generalizing hypothesis while preserving the privacy of each individual. In 2008, Kasiviswanathan et al. (FOCS 2008) gave a generic construction of private learners, in which the sample complexity is (generally) higher than what is needed for non-private learners. This gap in the sample complexity was then

Let \({\mathcal {C}}\) and \({\mathcal {D}}\) be hereditary graph classes. Consider the following problem: given a graph \(G\in {\mathcal {D}}\), find a largest, in terms of the number of vertices, induced subgraph of G that belongs to \({\mathcal {C}}\). We prove that it can be solved in \(2^{o(n)}\) time, where n is the number of vertices of G, if the following conditions are satisfied: the graphs

For an integer t, we let \(P_t\) denote the t-vertex path. We write \(H+G\) for the disjoint union of two graphs H and G, and for an integer r and a graph H, we write rH for the disjoint union of r copies of H. We say that a graph G is H-free if no induced subgraph of G is isomorphic to the graph H. In this paper, we study the complexity of k-coloring, for a fixed integer k, when restricted to the

We address the problem of speeding up group computations in cryptography using a single untrusted computational resource. We analyze the security of two efficient protocols for securely outsourcing (multi-)exponentiations. We show that the schemes do not achieve the claimed security guarantees and we present practical polynomial-time attacks on the delegation protocols which allow the untrusted helper

After publication of the article [1] the authors have noticed that the funding information are not published in online and print version of the article. The omitted funding acknowledgement is given below.

This paper addresses the problem of designing a \(\beta \)-additive fault-tolerant approximate BFS (or FT-ABFS for short) structure, namely, a subgraph H of the network G such that subsequent to the failure of a single edge e, the surviving part of H still contains an approximate BFS spanning tree for (the surviving part of) G, whose distances satisfy \(\mathrm{dist}(s,v,H{\setminus } \{e\}) \le \mathrm{dist}(s

Flip graphs are a ubiquitous class of graphs, which encode relations on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance, are the graphs induced by quadrilateral flips in triangulations of a convex polygon. For some definition of a flip graph, a natural computational problem to consider is the flip distance: Given two objects, what is the minimum

A robot modeled as a deterministic finite automaton has to build a structure from material available to it. The robot navigates in the infinite oriented grid \({\mathbb {Z}} \times {\mathbb {Z}}\). Some cells of the grid are full (contain a brick) and others are empty. The subgraph of the grid induced by full cells, called the shape, is initially connected. The (Manhattan) distance between the furthest

We introduce a dynamic version of the NP-hard graph modification problem Cluster Editing. The essential point here is to take into account dynamically evolving input graphs: having a cluster graph (that is, a disjoint union of cliques) constituting a solution for a first input graph, can we cost-efficiently transform it into a “similar” cluster graph that is a solution for a second (“subsequent”) input

In the article Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints, we claimed a worst-case runtime of and for the Multi-Objective Evolutionary Algorithm and the Multi-Objective Genetic Algorithm, respectively, on linear profit functions under dynamic uniform constraint, where denotes the difference between the original constraint bound B and

Applications designed for data-parallel computation frameworks such as MapReduce usually alternate between computation and communication stages. Coflow scheduling is a recent popular networking abstraction introduced to capture such application-level communication patterns in datacenters. In this framework, a datacenter is modeled as a single non-blocking switch with m input ports and m output ports

It is generally accepted that populations are useful for the global exploration of multi-modal optimisation problems. Indeed, several theoretical results are available showing such advantages over single-trajectory search heuristics. In this paper we provide evidence that evolving populations via crossover and mutation may also benefit the optimisation time for hillclimbing unimodal functions. In particular

Given two strings S and T, each of length at most n, the longest common substring (LCS) problem is to find a longest substring common to S and T. This is a classical problem in computer science with an \(\mathcal {O}(n)\)-time solution. In the fully dynamic setting, edit operations are allowed in either of the two strings, and the problem is to find an LCS after each edit. We present the first solution

We introduce a novel adversarial model for scheduling with explorable uncertainty. In this model, the processing time of a job can potentially be reduced (by an a priori unknown amount) by testing the job. Testing a job j takes one unit of time and may reduce its processing time from the given upper limit \(\bar{p}_j\) (which is the time taken to execute the job if it is not tested) to any value between

Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For m-edge and n-vertex graphs, it is well-known to be solvable in \(O(m\sqrt{n})\) time; however, for several applications this running time is still too slow. We investigate how linear-time (and almost linear-time) data reduction (used as preprocessing) can alleviate the situation. More

We study Subgraph Isomorphism on graph classes defined by a fixed forbidden graph. Although there are several ways for forbidding a graph, we observe that it is reasonable to focus on the minor relation since other well-known relations lead to either trivial or equivalent problems. When the forbidden minor is connected, we present a near dichotomy of the complexity of Subgraph Isomorphism with respect

Despite significant progress in the theory of evolutionary algorithms, the theoretical understanding of evolutionary algorithms which use non-trivial populations remains challenging and only few rigorous results exist. Already for the most basic problem, the determination of the asymptotic runtime of the \((\mu +\lambda )\) evolutionary algorithm on the simple OneMax benchmark function, only the special

In this work, we first study a natural generalisation of the Min-Cut problem, where a graph is augmented by a superadditive set function defined on its vertex subsets. The goal is to select a vertex subset such that the weight of the induced cut plus the set function value are minimised. In addition, a lower and upper bound is imposed on the solution size. We present a polynomial-time algorithm for

Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string matching is an efficient approach recently introduced in order to overcome the prohibitive space requirements of an index construction, on the one hand, and drastically

We derandomize Valiant’s (J ACM 62, Article 13, 2015) subquadratic-time algorithm for finding outlier correlations in binary data. This demonstrates that it is possible to perform a deterministic subquadratic-time similarity join of high dimensionality. Our derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range as Valiant’s randomized algorithm, but

Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach et al. (27th symposium on discrete algorithms (SODA), pp 1306–1325, 2016) introduced two natural deterministic conditions: (1) a power-law upper bound on the degree distribution (PLB-U)

The bin covering problem asks for covering a maximum number of bins with an online sequence of n items of different sizes in the range (0, 1]; a bin is said to be covered if it receives items of total size at least 1. We study this problem in the advice setting and provide asymptotically tight bounds of \(\Theta (n \log {\textsc {Opt}})\) on the size of advice required to achieve optimal solutions

We study a scheduling problem arising in demand response management in smart grid. Consumers send in power requests with a flexible feasible time interval during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective

In this paper, we investigate the complexity of Maximum Independent Set (MIS) in the class of H-free graphs, that is, graphs excluding a fixed graph as an induced subgraph. Given that the problem remains NP-hard for most graphs H, we study its fixed-parameter tractability and make progress towards a dichotomy between FPT and W[1]-hard cases. We first show that MIS remains W[1]-hard in graphs forbidding

We propose and analyze a self-adaptive version of the \((1,\lambda )\) evolutionary algorithm in which the current mutation rate is encoded within the individual and thus also subject to mutation. A rigorous runtime analysis on the OneMax benchmark function reveals that a simple local mutation scheme for the rate leads to an expected optimization time (number of fitness evaluations) of \(O(n\lambda

A (possibly degenerate) drawing of a graph G in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing whether a piece-wise linear drawing of a planar graph G in the plane is approximable by an embedding can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class. In other words

A space bounded \( O(d/\log d)\)-competitive hypercube packing algorithm with one active bin only is presented. As a starting point we give a simple 1-space bounded hypercube packing algorithm with competitive ratio \( (3/2)^{d}+O((21/16)^d)\), for \(d\ge 3.\)

A mobile agent equipped with a compass and a measure of length has to find an inert treasure in the Euclidean plane. Both the agent and the treasure are modeled as points. In the beginning, the agent is at a distance at most \(D>0\) from the treasure, but knows neither the distance nor any bound on it. Finding the treasure means getting at distance at most 1 from it. The agent makes a series of moves

In this paper, we study the problem of opening centers to cluster a set of clients in a metric space so as to minimize the sum of the costs of the centers and of the cluster radii, in a dynamic environment where clients arrive and depart, and the solution must be updated efficiently while remaining competitive with respect to the current optimal solution. We call this dynamic sum-of-radii clustering

The k-leaf power graph G of a tree T is a graph whose vertices are the leaves of T and whose edges connect pairs of leaves at unweighted distance at most k in T. Recognition of the k-leaf power graphs for \(k \ge 7\) is still an open problem. In this paper, we provide two algorithms for this problem for sparse leaf power graphs. Our results shows that the problem of recognizing these graphs is fixed-parameter

Lempel–Ziv (LZ77 or, briefly, LZ) is one of the most effective and widely-used compressors for repetitive texts. However, the existing efficient methods computing the exact LZ parsing have to use linear or close to linear space to index the input text during the construction of the parsing, which is prohibitive for long inputs. An alternative is Relative Lempel–Ziv (RLZ), which indexes only a fixed

Given a simple graph \(G = (V, E)\) and a constant integer \(k \ge 2\), the k-path vertex cover problem (PkVC) asks for a minimum subset \(F \subseteq V\) of vertices such that the induced subgraph \(G[V - F]\) does not contain any path of order k. When \(k = 2\), this turns out to be the classic vertex cover (VC) problem, which admits a \(\left( 2 - {\Theta }\left( \frac{1}{\log |V|}\right) \right)\)-approximation

The Maximum Carpool Matching problem is a star packing problem in directed graphs. Formally, given a directed graph \(G = (V, A)\), a capacity function \(c: V \rightarrow {\mathbb {N}}\), and a weight function \(w: A \rightarrow {\mathbb {R}}^+\), a carpool matching is a subset of arcs, \(M \subseteq A\), such that every \(v \in V\) satisfies: (1) \(d^{\text {in}}_{M}(v) \cdot d^{\text {out}}_{M}(v)

We introduce the inverse Voronoi diagram problem in graphs: given a graph G with positive edge-lengths and a collection \({\mathbb {U}}\) of subsets of vertices of V(G), decide whether \({\mathbb {U}}\) is a Voronoi diagram in G with respect to the shortest-path metric. We show that the problem is NP-hard, even for planar graphs where all the edges have unit length. We also study the parameterized

The problem of truth discovery arises in many areas such as database, data mining, data crowdsourcing and machine learning. It seeks trustworthy information from possibly conflicting data provided by multiple sources. Due to its practical importance, the problem has been studied extensively in recent years. Two competing models were proposed for truth discovery, weight-based model and probabilistic

A graph G is called a pairwise compatibility graph (PCG, for short) if it admits a tuple \((T,w, d_{\min },d_{\max })\) of a tree T whose leaf set is equal to the vertex set of G, a non-negative edge weight w, and two non-negative reals \(d_{\min }\le d_{\max }\) such that G has an edge between two vertices \(u,v\in V\) if and only if the distance between the two leaves u and v in the weighted tree

We prove that, given two topologically-equivalent upward planar straight-line drawings of an n-vertex directed graph G, there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of O(1) morphing steps if G is a reduced planar st-graph, O(n) morphing steps if G is a planar st-graph, O(n) morphing steps if

In this work we study the problem of collecting protected data in ad-hoc sensor network using a mobile entity called MULE. The objective is to increase information survivability in the network. Sensors from all over the network, route their sensing data through a data gathering tree, towards a particular node, called the sink. In case of a failed sensor, all the aggregated data from the sensor and

This paper is dedicated to the counting problem of writing an integer number z as a sum of an ordered sequence of n integers from n given intervals, i.e., counting the number of configurations \((z_1,\ldots ,z_n)\) with \(z = z_1 + \cdots + z_n\) for \(z_i \in [x_i, y_i]\) with integers \(x_i\) and \(y_i\) and \(1 \le i \le n\). We show an algorithm computing this number in \( \mathop {}\mathopen {}{\mathcal