Approximating max-min linear programs with local algorithms

A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms to max-min LPs where the objective is to maximise $\min_k \sum_v c_{kv} x_v$ subject to $\sum_v a_{iv} x_v \le 1$ for each $i$ and $x_v \ge 0$ for each $v$. Here $c_{kv} \ge 0$, $a_{iv} \ge 0$, and the support sets $V_i = \{v : a_{iv} > 0 \}$, $V_k = \{v : c_{kv}>0 \}$, $I_v = \{i : a_{iv} > 0 \}$ and $K_v = \{k : c_{kv} > 0 \}$ have bounded size. In the distributed setting, each agent $v$ is responsible for choosing the value of $x_v$, and the communication network is a hypergraph $\mathcal{H}$ where the sets $V_k$ and $V_i$ constitute the hyperedges. We present inapproximability results for a wide range of structural assumptions; for example, even if $|V_i|$ and $|V_k|$ are bounded by some constants larger than 2, there is no local approximation scheme. To contrast the negative results, we present a local approximation algorithm which achieves good approximation ratios if we can bound the relative growth of the vertex neighbourhoods in $\mathcal{H}$.Comment: 16 pages, 2 figure

A systematic exercise tool helps researchers ponder the ethical implications of AI

In addition to many clear benefits, AI technology can also bring risks related to the misuse of technology and for example increased inequalities. There is thus an increased demand to apply the principles of human-centricity and ethics in the development of AI. Members of the Ethics Advisory Board of the Finnish Centre for Artificial Intelligence (FCAI) have developed an Ethics Exercise Tool to help AI researchers consider and discuss the ethical implications of their research and strengthen ethical understanding within their team

Directing and Combining Multiple Queries for Exploratory Search by Visual Interactive Intent Modeling

In interactive information-seeking, a user often performs many interrelated queries and interactions covering multiple aspects of a broad topic of interest. Especially in difficult information-seeking tasks the user may need to find what is in common among such multiple aspects. Therefore, the user may need to compare and combine results across queries. While methods to combine queries or rankings have been proposed, little attention has been paid to interactive support for combining multiple queries in exploratory search. We introduce an interactive information retrieval system for exploratory search with multiple simultaneous search queries that can be combined. The user is able to direct search in the multiple queries, and combine queries by two operations: intersection and difference, which reveal what is relevant to the user intent of two queries, and what is relevant to one but not the other. Search is directed by relevance feedback on visualized user intent models of each query. Operations on queries act directly on the intent models inferring a combined user intent model. Each combination yields a new result (ranking) and acts as a new search that can be interactively directed and further combined. User experiments on difficult information-seeking tasks show that our novel system with query operations yields more relevant top-ranked documents in a shorter time than a baseline multiple-query system.Peer reviewe

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

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.Peer reviewe

An optimal local approximation algorithm for max-min linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0 for nonnegative matrices A and C. We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.Peer reviewe

Local approximability of max-min and min-max linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0. In a min-max LP, the objective is to minimise ρ subject to Ax ≤ ρ1, Cx ≥ 1, and x ≥ 0. The matrices A and C are nonnegative and sparse: each row ai of A has at most ΔI positive elements, and each row ck of C has at most ΔK positive elements. We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms). We show that for any ΔI ≥ 2, ΔK ≥ 2, and ε > 0 there exists a local algorithm that achieves the approximation ratio ΔI (1 − 1/ΔK) + ε. We also show that this result is the best possible: no local algorithm can achieve the approximation ratio ΔI (1 − 1/ΔK) for any ΔI ≥ 2 and ΔK ≥ 2.Peer reviewe

Digital Me : Controlling and Making Sense of My Digital Footprint

Peer reviewe