David Peleg

Weizmann Institute of Science | weizmann · Department of Computer Science and Applied Mathematics

The problem of realizing a given degree sequence by a multigraph can be thought of as a relaxation of the classical degree realization problem (where the realizing graph is simple). This paper concerns the case where the realizing multigraph is required to be bipartite.The problem of characterizing degree sequences that can be realized by a biparti...

The paper considers the SUPPORTED model of distributed computing introduced by Schmid and Suomela [HotSDN'13], generalizing the LOCAL and CONGEST models. In this framework, multiple instances of the same problem, differing from each other by the subnetwork to which they apply, recur over time, and need to be solved efficiently online. To do that, o...

Network realization problems require, given a specification π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} for some network parameter (such as de...

This paper presents and studies a generalization of the microscopic image reconstruction problem (MIR) introduced by Frosini and Nivat (2007) and Nivat (2002). Consider a specimen for inspection, represented as a collection of points typically organized on a grid in the plane. Assume each point x has an associated physical value ℓx, which we would...

A singularly (near) optimal distributed algorithm is one that is (near) optimal in \emph{two} criteria, namely, its time and message complexities. For \emph{synchronous} CONGEST networks, such algorithms are known for fundamental distributed computing problems such as leader election [Kutten et al., JACM 2015] and Minimum Spanning Tree (MST) constr...

The n-player Hotelling game calls for each player to choose a point on the line segment, so as to maximize the size of his Voronoi cell. This paper studies the Hotelling game in fault-prone settings. Two fault models are studied: line faults and player faults. The first model assumes that the environment is prone to failure: with some probability,...

Consider the following natural variation of the degree realization problem. Let G=(V,E) be a simple undirected graph of order n. Let f∈R≥0n be a vector of vertex requirements, and let w∈R≥0n be a vector of provided services at the vertices. Then w satisfies f on G if the constraints ∑j∈N(i)wj=fi are satisfied for all i∈V, where N(i) denotes the nei...

Consider the following natural variation of the degree realization problem. Let \(G=(V, E)\) be a simple undirected graph of order n. Let \(f \in \mathbb {R}_{\ge 0}^{n}\) be a vector of vertex requirements, and let \(w\in \mathbb {R}_{\ge 0}^{n}\) be a vector of provided services at the vertices. Then w satisfies f on G if the constraints \(\sum _...

Theoretical study of optimization problems in wireless communication often deals with tasks that concern a single point. For example, the power control problem requires computing a power assignment guaranteeing that each transmitting station s i is successfully received at a single receiver point r i . This paper aims at addressing communication ap...

We study graph realization problems for the first time from a distributed perspective. Graph realization problems are encountered in distributed construction of overlay networks that must satisfy certain degree or connectivity properties. We study them in the node capacitated clique (NCC) model of distributed computing, recently introduced for repr...

This paper concerns designing distributed algorithms that are {\em singularly optimal}, i.e., algorithms that are {\em simultaneously} time and message {\em optimal}, for the fundamental leader election problem in {\em asynchronous} networks. Kutten et al. (JACM 2015) presented a singularly near optimal randomized leader election algorithm for gene...

We study the {\em Budgeted Dominating Set} (BDS) problem on uncertain graphs, namely, graphs with a probability distribution $p$ associated with the edges, such that an edge $e$ exists in the graph with probability $p(e)$. The input to the problem consists of a vertex-weighted uncertain graph $\G=(V, E, p, \omega)$ and an integer {\em budget} (or {...

This paper concerns the behavior of an SINR diagram of wireless systems, composed of a set S of n stations embedded in Rd, when restricted to the corresponding Voronoi diagram imposed on S. The diagram obtained by restricting the SINR zones to their corresponding Voronoi cells is referred to hereafter as an SINR+Voronoi diagram. Uniform SINR diagra...

A network realization problem involves a given specification for some network parameters (such as vertex degrees or inter-vertex distances), and requires constructing a network G that satisfies , if possible. In many settings, it may be difficult or impossible to come up with a precise realization (e.g., the specification data might be inaccurate,...

Network realization problems require, given a specification for some network parameter (such as degrees, distances or connectivity), to construct a network G conforming to , or to determine that no such network exists. In this paper we study composed profile realization, where the given instance consists of two or more profile specifications that n...

Given a degree sequence d of length n, the Degree Realization problem is to decide if there exists a graph whose degree sequence is d, and if so, to construct one such graph. Consider the following natural variant of the problem. Let \(G=(V, E)\) be a simple undirected graph of order n. Let \(f \in \mathbb {R}_{\ge 0}^{n}\) be a vector of vertex re...

Assume that we inspect a specimen represented as a collection of points. The points are typically organized on a grid structure in 2D- or 3D-space, and each point has an associated physical value. The goal of the inspection is to determine these values. Yet, measuring these values directly (by surgical probes) may damage the specimen or is simply i...

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 sati...

This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in networks. Our main result is a randomized distributed leader election algorithm for asynchronous complete networks that is essentially (up to a polylogari...

We study the mixed approach to fault tolerance in the general context of server assignment in networks. The approach is based on mixing two different existing strategies, namely, reinforcement and backup. The former strategy protects clients by reinforcing the servers assigned to them and making them fault-resistant, possibly at a high cost, while...

Individuals in social networks tend to exhibit homophily in their social ties, namely, they prefer bonding with others of the same social group (e.g., the same nationality, gender, socio-economic background, etc.). To formalize this phenomenon in the context of an evolving social network, we consider a mixed preferential attachment (MPA), bi-popula...

We study graph realization problems from a distributed perspective and we study it in the node capacitated clique (NCC) model of distributed computing, recently introduced for representing peer-to-peer networks. We focus on two central variants, degree-sequence realization and minimum threshold-connectivity realization both of which result in overl...

We consider the problem of realizable interval-sequences. An interval sequence comprises of $n$ integer intervals $[a_i,b_i]$ such that $0\leq a_i \leq b_i \leq n-1$, and is said to be graphic/realizable if there exists a graph with degree sequence, say, $D=(d_1,\ldots,d_n)$ satisfying the condition $a_i \leq d_i \leq b_i$, for each $i \in [1,n]$....

The classical problem of degree sequence realizability asks whether or not a given sequence of $n$ positive integers is equal to the degree sequence of some $n$-vertex undirected simple graph. While the realizability problem of degree sequences has been well studied for different classes of graphs, there has been relatively little work concerning t...

The classical Hotelling game is played on a line segment whose points represent uniformly distributed clients. The n players of the game are servers who need to place themselves on the line segment, and once this is done, each client gets served by the player closest to it. The goal of each player is to choose its location so as to maximize the num...

Given a degree sequence d¯ of length n, the degree realization problem is to decide if d¯ has a realization, namely, an n-vertex graph whose degree sequence is d¯, and if so, to construct one such realization. The problem was well researched over the recent decades and plays an important role in the field of Social Networks. In this paper, we consi...

The classical Hotelling game is played on a line segment whose points represent uniformly distributed clients. The $n$ players of the game are servers who need to place themselves on the line segment, and once this is done, each client gets served by the player closest to it. The goal of each player is to choose its location so as to maximize the n...

The Hotelling game consists of n servers each choosing a point on the line segment, so as to maximize the amount of clients it attracts. Clients are uniformly distributed along the line, and each client buys from the closest server. In this paper, we study a fault-prone version of the Hotelling game, where the line fails at multiple random location...

We consider shortest paths computation and related tasks from the viewpoint of network algorithms, where the n-node input graph is also the computational system: nodes represent processors and edges represent communication links, which can in each time step carry an \(\mathcal {O}(\log n)\)-bit message. We identify several basic distributed distanc...

Occasionaly, every society needs to reach a decision among its members. For this, it may use a voting mechanism, i.e., collect the votes of the group members and output a decision that best expresses the group's will. To make up their minds, individuals often discuss the issue with friends before taking their votes, thus mutually affecting each oth...

The n-player Hotelling game calls for each player to choose a point on the line segment, so as to maximize the size of his Voronoi cell. This paper studies fault-tolerant versions of the Hotelling game. Two fault models are studied. The first assumes that the environment is prone to failure: with some probability, a disconnection occurs at a random...

We present a uniform approach to derive message-time tradeoffs and message lower bounds for synchronous distributed computations using results from communication complexity theory. Since the models used in the classical theory of communication complexity are inherently asynchronous, lower bounds do not directly apply in a synchronous setting. To ad...

A common two-tier structure for social networks is based on partitioning society into two parts, referred to as the elite and the periphery, where the “elite” is the relatively small but well-connected and highly influential group of powerful individuals around which the society is centered, and the “periphery” consists of the rest of society. It i...

Elites in social networks—Datasets information. (PDF)

This paper introduces an extended notion of expansion suitable for radio networks. A graph G=(V,E) is said to be an (α_w, β_w) -\em wireless expander if for every subset S \subseteq V s.t. |S|łeq α_w \cdot |V| , there exists a subset S'\subseteq S s.t. there are at least β_w \cdot |S| vertices in V\backslash S that are adjacent in G to exactly one...

The study of graphs and networks often involves studying various parameters of the graph vertices, capturing different aspects of the graph structure, such as the vertex degrees or the distances between the vertices. Given an n-vertex graph G and a parameter of interest f, one may associate with G a vector \(\mathcal{F}(G)=\langle f_1,\ldots ,f_n\r...

We study the mixed approach to fault tolerance in the general context of server assignment in networks. The approach is based on mixing two different existing strategies, namely, reinforcement and backup. The former strategy protects clients by reinforcing the servers assigned to them and making them fault-resistant (at a possibly high cost), while...

This paper demonstrates that the Preferential Attachment rule naturally emerges in the context of evolutionary network formation, as the unique Nash equilibrium of a simple social network game. In this game, each node aims at maximizing its degree in the future, representing its social capital in the "society" formed by the nodes and their connecti...

We investigate two NP-complete vertex partition problems on edge-weighted complete graphs with 3k vertices. The first problem asks to partition the graph into k vertex disjoint paths of length 2 (referred to as 2-paths) such that the total weight of the paths is maximized. We present a cubic time approximation algorithm that computes a 2-path parti...

This paper introduces an extended notion of expansion suitable for radio networks. A graph $G=(V,E)$ is called an $(\alpha_w, \beta_w)$-{wireless expander} if for every subset $S \subseteq V$ s.t. $|S|\leq \alpha_w \cdot |V|$, there exists a subset $S'\subseteq S$ s.t. there are at least $\beta_w \cdot |S|$ vertices in $V\backslash S$ adjacent in $...

A fault-tolerant structure for a network is required to continue functioning following the failure of some of the network’s edges or vertices. This article addresses the problem of designing a fault-tolerant (α , β) approximate BFS structure (or FT-ABFS structure for short), namely, a subgraph H of the network G such that subsequent to the failure...

The $n$-player Hotelling game calls for each player to choose a point on the line segment, so as to maximize the size of his Voronoi cell. This paper studies fault-tolerant versions of the Hotelling game. Two fault models are studied: line faults and player faults. The first model assumes that the environment is prone to failure: with some probabil...

This note considers a 1-dimensional wireless network consisting of a set of n stations located on a line, in the SINR model, which compares the received power of a signal at a receiver against the sum of strengths of other interfering signals plus background noise. The behavior of a multi-station network is described using the convenient representa...

It is known that individuals in social networks tend to exhibit homophily (a.k.a. assortative mixing) in their social ties, which implies that they prefer bonding with others of their own kind. But what are the reasons for this phenomenon? Is it that such relations are more convenient and easier to maintain? Or are there also some more tangible ben...

Consider a random preferential attachment model G(p) for network evolution that allows both node and edge arrivals. Starting with an arbitrary nonempty graph G0, at each time step, there are two possible events: with probability p > 0 a new node arrives and a new edge is added between the new node and an existing node, and with probability 1 - p a...

Area coverage is an important task for mobile robots, mainly due to its applicability in many domains, such as search and rescue. In this paper we study the problem of multi-robot coverage, in which the robots must obey a strong communication restriction: they should maintain connectivity between teammates throughout the coverage. We formally descr...

Population control policies are proposed and in some places employed as a means towards curbing population growth. This paper is concerned with a disturbing side-effect of such policies, namely, the potential risk of societal fragmentation due to changes in the distribution of family sizes. This effect is illustrated in some simple settings and dem...

Recent evidence shows that in many societies the relative sizes of the economic and social elites are continuously shrinking. Is this a natural social phenomenon? We try to address this question by studying a special case of a core-periphery structure composed of a social elite, namely, a relatively small but well-connected and highly influential g...

This paper attempts to rigorously analyze the social effects of power inequality and glass ceiling in a society with two populations (e.g. men and women). To this end, we define a mathematical model based on a social network with two populations, in which these phenomena are studied. We define measures for Normalized (or Differential) Power Inequal...

It is known that individuals in social networks tend to exhibit homophily (a.k.a. assortative mixing) in their social ties, which implies that they prefer bonding with others of their own kind. But what are the reasons for this phenomenon? Is it that such relations are more convenient and easier to maintain? Or are there also some more tangible ben...

Population control policies are proposed and in some places employed as a means towards curbing population growth. This paper is concerned with a disturbing side-effect of such policies, namely, the potential risk of societal fragmentation due to changes in the distribution of family sizes. This effect is illustrated in some simple settings and dem...

Consider a setting where possibly sensitive information sent over a path in a network is visible to every neighbor of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a path P can be measured as the number of nodes adjacent to it, denoted by N[P]. A path is said to be secluded if...

The paper studies broadcasting in radio networks whose stations are represented by points in the Euclidean plane (each station knows its own coordinates). In any given time step, a station can either receive or transmit. A message transmitted from station v is delivered to every station u at distance at most 1 from v, but u successfully hears the m...

A fault-tolerant structure for a network is required for continued functioning following the failure of some of the network's edges or vertices. This article considers breadth-first search (BFS) spanning trees and addresses the problem of designing a sparse fault-tolerant BFS structure (FT-BFS structure), namely, a sparse subgraph T of the given ne...

Inspired by social networks and complex systems, we propose a core-periphery network architecture that supports fast computation for many distributed algorithms, is robust and uses a linear number of links. Rather than providing a concrete network model, we take an axiom-based design approach. We provide three intuitive and independent algorithmic...

In this paper we study the reception zones of a wireless network in the SINR model with receivers that employ interference cancellation (IC), a technique that allows a receiver to decode interfering signals, and cancel them from the received signal in order to decode its intended message. We first derive some important topological properties of the...

We present a uniform approach to derive message-time tradeoffs and message lower bounds for synchronous distributed computations using results from communication complexity theory. Since the models used in the classical theory of communication complexity are inherently asynchronous, lower bounds do not directly apply in a synchronous setting. To ad...

How do the social graphs of Technical Program Committees of conferences look like? and how can studying these social graphs help us to decide whether there is a bias in paper selection processes for conferences? This work empirically studies the structure of program committees’ social graphs, their unique structure and characteristics, and examines...

The paper concerns time-efficient k-shot broadcasting in undirected radio networks for n-node graphs of diameter D. In a k-shot broadcasting algorithm, each node in the network is allowed to transmit at most k times. Both known and unknown topology models are considered. For the known topology model, the problem has been studied before by Gaąsienie...

We analyze the domination game, where two players, Dominator and Staller, construct together a dominating set M in a given graph, by alternately selecting vertices into M. Each move must increase the size of the dominated set. The players have opposing goals: Dominator wishes M to be as small as possible, and Staller has the opposite goal. Kinnersl...

This article proposes a forbidden-set labeling scheme for the family of unweighted graphs with doubling dimension bounded by α. For an n-vertex graph G in this family, and for any desired precision parameter ϵ > 0, the labeling scheme stores an O(1 + ϵ-1)2α log2 n-bit label at each vertex. Given the labels of two end-vertices s and t, and the label...

A distributed task is local if its time complexity is (nearly) constant, otherwise it is global. Unfortunately, local tasks are relatively scarce, and most distributed tasks require time at least logarithmic in the network size (and often higher than that). In a dynamic setting, i.e., when the network undergoes repeated and frequent topological cha...

This paper concerns the behavior of an SINR diagram of wireless systems, composed of a set S of n stations embedded in \(\mathbb R^d\), when restricted to the corresponding Voronoi diagram imposed on S. The diagram obtained by restricting the SINR zones to their corresponding Voronoi cells is referred to hereafter as an SINR+Voronoi diagram. While...

Is there a bias in paper selection processes for conferences? This work addresses one aspect of this question, and empirically examines if there is a bias in favor of the collaborators of the technical program committee members. Specifically, we check whether a paper written by a past collaborator of a program committee member is more likely to be...

We study the problem of using binary questions to identify a single truth teller from a collection of players, at most of whom may lie. Our focus is on trying to solve the problem using (or slightly more than ) questions, which is the fewest feasible number of questions. We also obtain a randomized solution for instances of the problem that are not...

Consider a preferential attachment model for network evolution that allows both node and edge arrival events: at time t, with probability \(p_t\) a new node arrives and a new edge is added between the new node and an existing node, and with probability \(1-p_t\) a new edge is added between two existing nodes. In both cases existing nodes are chosen...

We consider the SINR wireless model with uniform power. In this model the success of a transmission is determined by the ratio between the strength of the transmission signal and the noise produced by other transmitting processors plus ambient noise. The local broadcasting problem is a fundamental problem in this setting. Its goal is producing a sc...

In this review, we illustrate the relations between wireless communication and computational geometry. As a concrete example, we consider a fundamental geometric object from each field: SINR diagrams and Voronoi diagrams. We discuss the relations between these representations, which appear in several distinct settings of wireless communication, as...

This paper initiates the study of fault resilient network structures that mix two orthogonal protection mechanisms:(a) backup, namely, augmenting the structure with many (redundant) low-cost but fault-prone components, and (b) reinforcement, namely, acquiring high-cost but fault-resistant components. To study the trade-off between these two mechani...

Graph spanners are sparse subgraphs that preserve the distances of the original graph up to some approximation ratio (the spanner's stretch). A number of algorithms are known for constructing sparse spanners with small multiplicative or additive stretch. Recently, algorithms were introduced for constructing fault-tolerant multiplicative spanners of...

This paper initiates the study of fault resilient network structures that mix two orthogonal protection mechanisms: (a) {\em backup}, namely, augmenting the structure with many (redundant) low-cost but fault-prone components, and (b) {\em reinforcement}, namely, acquiring high-cost but fault-resistant components. To study the trade-off between thes...

Graph spanners are sparse subgraphs that preserve the distances of the original graph, up to some small multiplicative factor or additive term (known as the stretch of the spanner). A number of algorithms are known for constructing sparse spanners with small multiplicative or additive stretch. Recently, the problem of constructing fault-tolerant mu...

The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment evolution model than by the ordinary (uniform) evolution lodel. Analogously, this paper extends the random {\em h...

The glass ceiling effect has been defined in a recent US Federal Commission report as "the unseen, yet unbreakable barrier that keeps minorities and women from rising to the upper rungs of the corporate ladder, regardless of their qualifications or achievements". It is well documented that many societies and organizations exhibit a glass ceiling. I...

We consider a simple model for reputation systems such as the one used by eBay. In our model there aren players, some of which may exhibit arbitrarily malicious (Byzantine) behavior, and there arem objects, some of which are bad. The goal of the honest players is to find a good object. To facilitate collaboration, the system maintains a shared bill...

We investigate two NP-complete vertex partition problems on edge weighted complete graphs with 3k vertices. The first problem asks to partition the graph into k vertex disjoint paths of length 2 (referred to as 2-paths) such that the total weight of the paths is maximized. We present a cubic time approximation algorithm that computes a 2-path parti...

The Perron–Frobenius (PF) theorem provides a simple characterization of the eigenvectors and eigenvalues of irreducible nonnegative square matrices. A generalization of the PF theorem to nonsquare matrices, which can be interpreted as representing systems with additional degrees of freedom, was recently presented in [1]. This generalized theorem re...

Recent evidence shows that in many societies worldwide the relative sizes of the economic and social elites are continuously shrinking. Is this a natural social phenomenon? What are the forces that shape this process? We try to address these questions by studying a Core-Periphery social structure composed of a social elite, namely, a relatively sma...