arXiv subjects

Piotr Skowron

Publications and source records attributed to Piotr Skowron.

62 records · Page 4Linked to original sources

arXiv2014

We Are Impatient: Algorithms for Geographically Distributed Load Balancing with (Almost) Arbitrary Load Functions

In geographically-distributed systems, communication latencies are non-negligible. The perceived processing time of a request is thus composed of the time needed to route the request to the server and the true processing time. Once a request reaches a target server, the processing time depends on the total load of that server; this dependency is described by a load function. We consider a broad class of load functions; we just require that they are convex and two times differentiable. In particular our model can be applied to heterogeneous systems in which every server has a different load function. This approach allows us not only to generalize results for queuing theory and for batches of requests, but also to use empirically-derived load functions, measured in a system under stress-testing. The optimal assignment of requests to servers is communication-balanced, i.e. for any pair of non perfectly-balanced servers, the reduction of processing time resulting from moving a single request from the overloaded to underloaded server is smaller than the additional communication latency. We present a centralized and a decentralized algorithm for optimal load balancing. We prove bounds on the algorithms' convergence. To the best of our knowledge these bounds were not known even for the special cases studied previously (queuing theory and batches of requests). Both algorithms are any-time algorithms. In the decentralized algorithm, each server balances the load with a randomly chosen peer. Such algorithm is very robust to failures. We prove that the decentralized algorithm performs locally-optimal steps. Our work extends the currently known results by considering a broad class of load functions and by establishing theoretical bounds on the algorithms' convergence. These results are applicable for servers whose characteristics under load cannot be described by a standard mathematical models.

cs.DC↗

arXiv2013

Achieving Fully Proportional Representation: Approximability Results

We study the complexity of (approximate) winner determination under the Monroe and Chamberlin--Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their representatives. The total (dis)satisfaction is calculated either as the sum of individual (dis)satisfactions (the utilitarian case) or as the (dis)satisfaction of the worst off voter (the egalitarian case). We provide good approximation algorithms for the satisfaction-based utilitarian versions of the Monroe and Chamberlin--Courant rules, and inapproximability results for the dissatisfaction-based utilitarian versions of them and also for all egalitarian cases. Our algorithms are applicable and particularly appealing when voters submit truncated ballots. We provide experimental evaluation of the algorithms both on real-life preference-aggregation data and on synthetic data. These experiments show that our simple and fast algorithms can in many cases find near-perfect solutions.

cs.AI↗

arXiv2013

Approximating the MaxCover Problem with Bounded Frequencies in FPT Time

We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The goal is to find up to K sets from S that jointly cover (i.e., include) as many elements as possible. This problem is well-known to be NP-hard and, under standard complexity-theoretic assumptions, the best possible polynomial-time approximation algorithm has approximation ratio (1 - 1/e). We first consider a variant of MaxCover with bounded element frequencies, i.e., a variant where there is a constant p such that each element belongs to at most p sets in S. For this case we show that there is an FPT approximation scheme (i.e., for each B there is a B-approximation algorithm running in FPT time) for the problem of maximizing the number of covered elements, and a randomized FPT approximation scheme for the problem of minimizing the number of elements left uncovered (we take K to be the parameter). Then, for the case where there is a constant p such that each element belongs to at least p sets from S, we show that the standard greedy approximation algorithm achieves approximation ratio exactly (1-e^{-max(pK/|S|, 1)}). We conclude by considering an unrestricted variant of MaxCover, and show approximation algorithms that run in exponential time and combine an exact algorithm with a greedy approximation. Some of our results improve currently known results for MaxVertexCover.

cs.DS↗

arXiv2013

The Complexity of Fully Proportional Representation for Single-Crossing Electorates

We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our algorithm for Chamberlin--Courant's rule can be modified to work for elections with bounded single-crossing width. To circumvent the hardness result for Monroe's rule, we consider single-crossing elections that satisfy an additional constraint, namely, ones where each candidate is ranked first by at least one voter (such elections are called narcissistic). For single-crossing narcissistic elections, we provide an efficient algorithm for the egalitarian version of Monroe's rule.

cs.GT↗

arXiv2013

Exploring heterogeneity of unreliable machines for p2p backup

P2P architecture is a viable option for enterprise backup. In contrast to dedicated backup servers, nowadays a standard solution, making backups directly on organization's workstations should be cheaper (as existing hardware is used), more efficient (as there is no single bottleneck server) and more reliable (as the machines are geographically dispersed). We present the architecture of a p2p backup system that uses pairwise replication contracts between a data owner and a replicator. In contrast to standard p2p storage systems using directly a DHT, the contracts allow our system to optimize replicas' placement depending on a specific optimization strategy, and so to take advantage of the heterogeneity of the machines and the network. Such optimization is particularly appealing in the context of backup: replicas can be geographically dispersed, the load sent over the network can be minimized, or the optimization goal can be to minimize the backup/restore time. However, managing the contracts, keeping them consistent and adjusting them in response to dynamically changing environment is challenging. We built a scientific prototype and ran the experiments on 150 workstations in the university's computer laboratories and, separately, on 50 PlanetLab nodes. We found out that the main factor affecting the quality of the system is the availability of the machines. Yet, our main conclusion is that it is possible to build an efficient and reliable backup system on highly unreliable machines (our computers had just 13% average availability).

cs.DC↗

arXiv2013

Fully Proportional Representation as Resource Allocation: Approximability Results

We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions, there are no constant-factor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (briefly put, these variants correspond to optimizing total voter satisfaction under Borda scores, within Monroe's and Chamberlin and Courant's voting systems).

cs.GT↗

arXiv2013

Achieving Fully Proportional Representation is Easy in Practice

We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe's and Chamberlin-Courant's rules. Our experiments, conducted both on real-life preference-aggregation data and on synthetic data, show that even very simple and fast algorithms can in many cases find near-perfect solutions. Our results confirm and complement very recent theoretical analysis of Skowron et al., who have shown good lower bounds on the quality of (some of) the algorithms that we study.

cs.MA↗

arXiv2012

Network delay-aware load balancing in selfish and cooperative distributed systems

We consider a request processing system composed of organizations and their servers connected by the Internet. The latency a user observes is a sum of communication delays and the time needed to handle the request on a server. The handling time depends on the server congestion, i.e. the total number of requests a server must handle. We analyze the problem of balancing the load in a network of servers in order to minimize the total observed latency. We consider both cooperative and selfish organizations (each organization aiming to minimize the latency of the locally-produced requests). The problem can be generalized to the task scheduling in a distributed cloud; or to content delivery in an organizationally-distributed CDNs. In a cooperative network, we show that the problem is polynomially solvable. We also present a distributed algorithm iteratively balancing the load. We show how to estimate the distance between the current solution and the optimum based on the amount of load exchanged by the algorithm. During the experimental evaluation, we show that the distributed algorithm is efficient, therefore it can be used in networks with dynamically changing loads. In a network of selfish organizations, we prove that the price of anarchy (the worst-case loss of performance due to selfishness) is low when the network is homogeneous and the servers are loaded (the request handling time is high compared to the communication delay). After relaxing these assumptions, we assess the loss of performance caused by the selfishness experimentally, showing that it remains low. Our results indicate that a network of servers handling requests can be efficiently managed by a distributed algorithm. Additionally, even if the network is organizationally distributed, with individual organizations optimizing performance of their requests, the network remains efficient.

cs.DC↗