arXiv subjects

Christina Fragouli

Publications and source records attributed to Christina Fragouli.

At least 55 records · Page 3Linked to original sources

arXiv2019

Polynomial-time Capacity Calculation and Scheduling for Half-Duplex 1-2-1 Networks

This paper studies the 1-2-1 half-duplex network model, where two half-duplex nodes can communicate only if they point `beams' at each other; otherwise, no signal can be exchanged or interference can be generated. The main result of this paper is the design of two polynomial-time algorithms that: (i) compute the approximate capacity of the 1-2-1 half-duplex network and, (ii) find the network schedule optimal for the approximate capacity. The paper starts by expressing the approximate capacity as a linear program with an exponential number of constraints. A core technical component consists of building a polynomial-time separation oracle for this linear program, by using algorithmic tools such as perfect matching polytopes and Gomory-Hu trees.

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arXiv2018

Regret vs. Bandwidth Trade-off for Recommendation Systems

We consider recommendation systems that need to operate under wireless bandwidth constraints, measured as number of broadcast transmissions, and demonstrate a (tight for some instances) tradeoff between regret and bandwidth for two scenarios: the case of multi-armed bandit with context, and the case where there is a latent structure in the message space that we can exploit to reduce the learning phase.

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arXiv2018

Privacy in Index Coding: $k$-Limited-Access Schemes

In the traditional index coding problem, a server employs coding to send messages to $n$ clients within the same broadcast domain. Each client already has some messages as side information and requests a particular unknown message from the server. All clients learn the coding matrix so that they can decode and retrieve their requested data. Our starting observation is that, learning the coding matrix can pose privacy concerns: it may enable a client to infer information about the requests and side information of other clients. In this paper, we mitigate this privacy concern by allowing each client to have limited access to the coding matrix. In particular, we design coding matrices so that each client needs only to learn some of (and not all) the rows to decode her requested message. By means of two different privacy metrics, we first show that this approach indeed increases the level of privacy. Based on this, we propose the use of $k$-limited-access schemes: given an index coding scheme that employs $T$ transmissions, we create a $k$-limited-access scheme with $T_k\geq T$ transmissions, and with the property that each client needs at most $k$ transmissions to decode her message. We derive upper and lower bounds on $T_k$ for all values of $k$, and develop deterministic designs for these schemes, which are universal, i.e., independent of the coding matrix. We show that our schemes are order-optimal when either $k$ or $n$ is large. Moreover, we propose heuristics that complement the universal schemes for the case when both $n$ and $k$ are small.

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arXiv2018

Distorting an Adversary's View in Cyber-Physical Systems

In Cyber-Physical Systems (CPSs), inference based on communicated data is of critical significance as it can be used to manipulate or damage the control operations by adversaries. This calls for efficient mechanisms for secure transmission of data since control systems are becoming increasingly distributed over larger geographical areas. Distortion based security, recently proposed as one candidate for CPSs security, is not only more appropriate for these applications but also quite frugal in terms of prior requirements on shared keys. In this paper, we propose distortion-based metrics to protect CPSs communication and show that it is possible to confuse adversaries with just a few bits of pre-shared keys.

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arXiv2018

Gaussian 1-2-1 Networks: Capacity Results for mmWave Communications

This paper proposes a new model for wireless relay networks referred to as "1-2-1 network", where two nodes can communicate only if they point "beams" at each other, while if they do not point beams at each other, no signal can be exchanged or interference can be generated. This model is motivated by millimeter wave communications where, due to the high path loss, a link between two nodes can exist only if beamforming gain at both sides is established, while in the absence of beamforming gain the signal is received well below the thermal noise floor. The main result in this paper is that the 1-2-1 network capacity can be approximated by routing information along at most $2N+2$ paths, where $N$ is the number of relays connecting a source and a destination through an arbitrary topology.

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arXiv2018

A Pliable Index Coding Approach to Data Shuffling

A promising research area that has recently emerged, is on how to use index coding to improve the communication efficiency in distributed computing systems, especially for data shuffling in iterative computations. In this paper, we posit that pliable index coding can offer a more efficient framework for data shuffling, as it can better leverage the many possible shuffling choices to reduce the number of transmissions. We theoretically analyze pliable index coding under data shuffling constraints, and design a hierarchical data-shuffling scheme that uses pliable coding as a component. We find benefits up to $O(ns/m)$ over index coding, where $ns/m$ is the average number of workers caching a message, and $m$, $n$, and $s$ are the numbers of messages, workers, and cache size, respectively.

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arXiv2018

Secure Communication over 1-2-1 Networks

This paper starts by assuming a 1-2-1 network, the abstracted noiseless model of mmWave networks that was shown to closely approximate the Gaussian capacity in [1], and studies secure communication. First, the secure capacity is derived for 1-2-1 networks where a source is connected to a destination through a network of unit capacity links. Then, lower and upper bounds on the secure capacity are derived for the case when source and destination have more than one beam, which allow them to transmit and receive in multiple directions at a time. Finally, secure capacity results are presented for diamond 1-2-1 networks when edges have different capacities.

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arXiv2018

Privacy in Index Coding: Improved Bounds and Coding Schemes

It was recently observed in [1], that in index coding, learning the coding matrix used by the server can pose privacy concerns: curious clients can extract information about the requests and side information of other clients. One approach to mitigate such concerns is the use of $k$-limited-access schemes [1], that restrict each client to learn only part of the index coding matrix, and in particular, at most $k$ rows. These schemes transform a linear index coding matrix of rank $T$ to an alternate one, such that each client needs to learn at most $k$ of the coding matrix rows to decode its requested message. This paper analyzes $k$-limited-access schemes. First, a worst-case scenario, where the total number of clients $n$ is $2^T-1$ is studied. For this case, a novel construction of the coding matrix is provided and shown to be order-optimal in the number of transmissions. Then, the case of a general $n$ is considered and two different schemes are designed and analytically and numerically assessed in their performance. It is shown that these schemes perform better than the one designed for the case $n=2^T-1$.

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arXiv2017

Making recommendations bandwidth aware

This paper asks how much we can gain in terms of bandwidth and user satisfaction, if recommender systems became bandwidth aware and took into account not only the user preferences, but also the fact that they may need to serve these users under bandwidth constraints, as is the case over wireless networks. We formulate this as a new problem in the context of index coding: we relax the index coding requirements to capture scenarios where each client has preferences associated with messages. The client is satisfied to receive any message she does not already have, with a satisfaction proportional to her preference for that message. We consistently find, over a number of scenarios we sample, that although the optimization problems are in general NP-hard, significant bandwidth savings are possible even when restricted to polynomial time algorithms.

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arXiv2017

Wireless Network Simplification: The Performance of Routing

Consider a wireless Gaussian network where a source wishes to communicate with a destination with the help of N full-duplex relay nodes. Most practical systems today route information from the source to the destination using the best path that connects them. In this paper, we show that routing can in the worst case result in an unbounded gap from the network capacity - or reversely, physical layer cooperation can offer unbounded gains over routing. More specifically, we show that for $N$-relay Gaussian networks with an arbitrary topology, routing can in the worst case guarantee an approximate fraction $\frac{1}{\left\lfloor N/2 \right\rfloor + 1}$ of the capacity of the full network, independently of the SNR regime. We prove that this guarantee is fundamental, i.e., it is the highest worst-case guarantee that we can provide for routing in relay networks. Next, we consider how these guarantees are refined for Gaussian layered relay networks with $L$ layers and $N_L$ relays per layer. We prove that for arbitrary $L$ and $N_L$, there always exists a route in the network that approximately achieves at least $\frac{2}{(L-1)N_L + 4}$ $\left(\mbox{resp.}\frac{2}{LN_L+2}\right)$ of the network capacity for odd $L$ (resp. even $L$), and there exist networks where the best routes exactly achieve these fractions. These results are formulated within the network simplification framework, that asks what fraction of the capacity we can achieve by using a subnetwork (in our case, a single path). A fundamental step in our proof is a simplification result for MIMO antenna selection that may also be of independent interest. To the best of our knowledge, this is the first result that characterizes, for general wireless network topologies, what is the performance of routing with respect to physical layer cooperation techniques that approximately achieve the network capacity.

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arXiv2017

Half-Duplex Routing is NP-hard

Routing is a widespread approach to transfer information from a source node to a destination node in many deployed wireless ad-hoc networks. Today's implemented routing algorithms seek to efficiently find the path/route with the largest Full-Duplex (FD) capacity, which is given by the minimum among the point-to-point link capacities in the path. Such an approach may be suboptimal if then the nodes in the selected path are operated in Half-Duplex (HD) mode. Recently, the capacity (up to a constant gap that only depends on the number of nodes in the path) of an HD line network i.e., a path) has been shown to be equal to half of the minimum of the harmonic means of the capacities of two consecutive links in the path. This paper asks the questions of whether it is possible to design a polynomial-time algorithm that efficiently finds the path with the largest HD capacity in a relay network. This problem of finding that path is shown to be NP-hard in general. However, if the number of cycles in the network is polynomial in the number of nodes, then a polynomial-time algorithm can indeed be designed.

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arXiv2017

A Polynomial-Time Algorithm for Pliable Index Coding

In pliable index coding, we consider a server with $m$ messages and $n$ clients where each client has as side information a subset of the messages. We seek to minimize the number of broadcast transmissions, so that each client can recover any one unknown message she does not already have. Previous work has shown that the pliable index coding problem is NP-hard and requires at most $\mathcal{O}(\log^2(n))$ broadcast transmissions, which indicates exponential savings over the conventional index coding that requires in the worst case $\mathcal{O}(n)$ transmissions. In this work, building on a decoding criterion that we propose, we first design a deterministic polynomial-time algorithm that can realize the exponential benefits, by achieving, in the worst case, a performance upper bounded by $\mathcal{O}(\log^2(n))$ broadcast transmissions. We extend our algorithm to the $t$-requests case, where each client requires $t$ unknown messages that she does not have, and show that our algorithm requires at most $\mathcal{O}(t\log(n)+\log^2(n))$ broadcast transmissions. We construct lower bound instances that require at least $Ω(\log(n))$ transmissions for linear pliable index coding and at least $Ω(t+\log(n))$ transmissions for the $t$-requests case, indicating that both our upper and lower bounds are polynomials of $\log(n)$ and differ within a factor of $\mathcal{O}(\log(n))$. Finally, we provide a probabilistic analysis and show that the required number of transmissions is almost surely $Θ(\log(n))$, as compared to $Θ(n/\log(n))$ for index coding. Our numerical experiments show that our algorithm outperforms existing algorithms for pliable index coding by up to $50\%$ less transmissions.

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arXiv2017

The Benefit of Being Flexible in Distributed Computation

In wireless distributed computing, networked nodes perform intermediate computations over data placed in their memory and exchange these intermediate values to calculate function values. In this paper we consider an asymmetric setting where each node has access to a random subset of the data, i.e., we cannot control the data placement. The paper makes a simple point: we can realize significant benefits if we are allowed to be "flexible", and decide which node computes which function, in our system. We make this argument in the case where each function depends on only two of the data messages, as is the case in similarity searches. We establish a percolation in the behavior of the system, where, depending on the amount of observed data, by being flexible, we may need no communication at all.

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arXiv2017

Network Simplification in Half-Duplex: Building on Submodularity

This paper explores the {\it network simplification} problem in the context of Gaussian Half-Duplex (HD) diamond networks. Specifically, given an $N$-relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best $k$-relay subnetwork, as a function of the full network capacity. The main focus of this work is on the case when $k=N-1$ relays are selected out of the $N$ possible ones. First, a simple algorithm, which removes the relay with the minimum capacity (i.e., the worst relay), is analyzed and it is shown that the remaining $(N-1)$-relay subnetwork has an approximate (i.e., optimal up to a constant gap) HD capacity that is at least half of the approximate HD capacity of the full network. This fraction guarantee is shown to be tight if only the single relay capacities are known, i.e., there exists a class of Gaussian HD diamond networks with $N$ relays where, by removing the worst relay, the subnetwork of the remaining $k=N-1$ relays has an approximate capacity equal to half of the approximate capacity of the full network. Next, this work proves a fundamental guarantee, which improves over the previous fraction: there always exists a subnetwork of $k=N-1$ relays that achieves at least a fraction $\frac{N-1}{N}$ of the approximate capacity of the full network. This fraction is proved to be tight and it is shown that any optimal schedule of the full network can be used by at least one of the $N$ subnetworks of $N-1$ relays to achieve a worst-case performance guarantee of $\frac{N-1}{N}$. Additionally, these results are extended to derive lower bounds on the fraction guarantee for general $k \in [1:N]$. The key steps in the proofs lie in the derivation of properties of submodular functions, which provide a combinatorial handle on the network simplification problem in Gaussian HD diamond networks.

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arXiv2017

Efficiently Finding Simple Schedules in Gaussian Half-Duplex Relay Line Networks

The problem of operating a Gaussian Half-Duplex (HD) relay network optimally is challenging due to the exponential number of listen/transmit network states that need to be considered. Recent results have shown that, for the class of Gaussian HD networks with N relays, there always exists a simple schedule, i.e., with at most N +1 active states, that is sufficient for approximate (i.e., up to a constant gap) capacity characterization. This paper investigates how to efficiently find such a simple schedule over line networks. Towards this end, a polynomial-time algorithm is designed and proved to output a simple schedule that achieves the approximate capacity. The key ingredient of the algorithm is to leverage similarities between network states in HD and edge coloring in a graph. It is also shown that the algorithm allows to derive a closed-form expression for the approximate capacity of the Gaussian line network that can be evaluated distributively and in linear time. Additionally, it is shown using this closed-form that the problem of Half-Duplex routing is NP-Hard.

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arXiv2017

Communication vs Distributed Computation: an alternative trade-off curve

In this paper, we revisit the communication vs. distributed computing trade-off, studied within the framework of MapReduce in [1]. An implicit assumption in the aforementioned work is that each server performs all possible computations on all the files stored in its memory. Our starting observation is that, if servers can compute only the intermediate values they need, then storage constraints do not directly imply computation constraints. We examine how this affects the communication-computation trade-off and suggest that the trade-off be studied with a predetermined storage constraint. We then proceed to examine the case where servers need to perform computationally intensive tasks, and may not have sufficient time to perform all computations required by the scheme in [1]. Given a threshold that limits the computational load, we derive a lower bound on the associated communication load, and propose a heuristic scheme that achieves in some cases the lower bound.

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arXiv2017

Preserving Privacy while Broadcasting: $k$-Limited-Access Schemes

Index coding employs coding across clients within the same broadcast domain. This typically assumes that all clients learn the coding matrix so that they can decode and retrieve their requested data. However, learning the coding matrix can pose privacy concerns: it may enable clients to infer information about the requests and side information of other clients [1]. In this paper, we formalize the intuition that the achieved privacy can increase by decreasing the number of rows of the coding matrix that a client learns. Based on this, we propose the use of $k$-limited-access schemes: given an index coding scheme that employs $T$ transmissions, we create a $k$-limited-access scheme with $T_k\geq T$ transmissions, and with the property that each client learns at most $k$ rows of the coding matrix to decode its message. We derive upper and lower bounds on $T_k$ for all values of $k$, and develop deterministic designs for these schemes for which $T_k$ has an order-optimal exponent for some regimes.

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arXiv2017

A Distortion Based Approach for Protecting Inferences

Eavesdropping attacks in inference systems aim to learn not the raw data, but the system inferences to predict and manipulate system actions. We argue that conventional information security measures can be ambiguous on the adversary's estimation abilities, and adopt instead a distortion based framework that enables to operate over a metric space. We show that requiring perfect distortion-based security is more frugal than requiring perfect information-theoretic secrecy even for block length one codes, offering in some cases unbounded gains. Within this framework, we design algorithms that enable to efficiently use shared randomness, and show that each bit of shared random key is exponentially useful in security.

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