Valentin Polishchuk

Improved Approximation Algorithms for Relay Placement

In the relay placement problemthe input is a set of sensors and a number ri¾? 1, the communication range of a relay. The objective is to place a minimum number of relays so that between every pair of sensors there is a path through sensors and/or relays such that the consecutive vertices of the path are within distance rif both vertices are relays and within distance 1 otherwise. We present a 3.11-approximation algorithm, and show that the problem admits no PTAS, assuming P

Airspace Throughput Analysis Considering Stochastic Weather

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Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

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A local 2-approximation algorithm for the vertex cover problem

The estimation of the capacity of an airspace region during weather events is an important part of air traffic management. This problem must be solved ahead of time with predicted traffic demands and weather forecasts. In order to capture the uncertainty of the weather, a stochastic weather model is used. We investigate the problem of estimating the maximum capacity of an airspace region by analyzing the sector airspace geometry and a stochastic weather model. Using algorithms for computing geometric flow capacity in 2-dimensional regions, we compute the maximum capacity for an airspace having a given (deterministic) set of weather constraints. Then, we extend our results to a stochastic weather model, obtaining analytical results for weather constraints that form constraints along a line segment (e.g., placed along the flow bottleneck or along a squall line) and obtaining simulation results for a more general two-dimensional stochastic weather model. Our results allow us to determine the probability distribution of the throughput capacity of an airspace, given a probabilistic weather forecast.

Optimization schemes for protective jamming

We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds.We apply our results to give a distributed (2+ε)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching.

A simple local 3-approximation algorithm for vertex cover

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

isBF: Scalable in-packet bloom filter based multicast

In this paper, we study strategies for allocating and managing friendly jammers, so as to create virtual barriers that would prevent hostile eavesdroppers from tapping sensitive wireless communication. Our scheme precludes the use of any encryption technique. Applications include domains such as (i) protecting the privacy of storage locations where RFID tags are used for item identification, (ii) secure reading of RFID tags embedded in credit cards, (iii) protecting data transmitted through wireless networks, sensor networks, etc. By carefully managing jammers to produce noise, we show how to reduce the SINR of eavesdroppers to below a threshold for successful reception, without jeopardizing network performance. We present algorithms targeted towards optimizing power allocation and number of jammers needed in several settings. Experimental simulations back up our results.

Capacity Estimation for Low Altitude Airspace

We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required.

Data transmission and base-station placement for optimizing the lifetime of wireless sensor networks

Abstract Bloom filter (BF) based forwarding was proposed recently in several protocol alternatives to IP multicast. Some of these protocols avoid the state in intermediate routers and leave the burden of scalability management to the multicast source and end-hosts. Still, the existing BF-based protocols have scalability limitations and require explicit network management as well as non-trivial functionality from the network components. In this work we address the scalability limitations of the BF-based forwarding protocols by partitioning end-hosts into clusters. We propose several algorithms to do the partitioning so as to decrease the overall traffic in the network. We evaluate our algorithms in a real Internet topology, demonstrating the ability of the proposed design to save up to 70% of traffic volume in the large-scale topology for big groups of subscribers, and up to 30% for small groups.

Optimization Schemes for Protective Jamming

This paper uses a threshold based mathematical definition to estimate capacity for future sUAS traffic in low altitude uncontrolled airspace based on safety and performance considerations. It is motivated by the need to assess the impact of large-scale close proximity unmanned aircraft operations on communities and existing manned airspace. We simulate unmanned traffic over urban areas and estimate metrics focused on safety and performance efficiency. The effect of increasing traffic density on the metrics shows that safety is potentially the most critical capacity determining factor of the two.