Yuyi Wang

An efficiently computable subgraph pattern support measure: counting independent observations

Graph support measures are functions measuring how frequently a given subgraph pattern occurs in a given database graph. An important class of support measures relies on overlap graphs. A major advantage of overlap-graph based approaches is that they combine anti-monotonicity with counting the occurrences of a subgraph pattern which are independent according to certain criteria. However, existing overlap-graph based support measures are expensive to compute. In this paper, we propose a new support measure which is based on a new notion of independence. We show that our measure is the solution to a sparse linear program, which can be computed efficiently using interior point methods. We study the anti-monotonicity and other properties of this new measure, and relate it to the statistical power of a sample of embeddings in a network. We show experimentally that, in contrast to earlier overlap-graph based proposals, our support measure makes it feasible to mine subgraph patterns in large networks.

An efficiently computable support measure for frequent subgraph pattern mining

Graph support measures are functions measuring how frequently a given subgraph pattern occurs in a given database graph. An important class of support measures relies on overlap graphs. A major advantage of the overlap graph based approaches is that they combine anti-monotonicity with counting occurrences of a pattern which are independent according to certain criteria. However, existing overlap graph based support measures are expensive to compute. In this paper, we propose a new support measure which is based on a new notion of independence. We show that our measure is the solution to a linear program which is usually sparse, and using interior point methods can be computed efficiently. We show experimentally that for large networks, in contrast to earlier overlap graph based proposals, pattern mining based on our support measure is feasible.

Minimum Cost Perfect Matching with Delays for Two Sources

We study a version of the online min-cost perfect matching with delays (MPMD) problem recently introduced by Emek et al. (STOC 2016). In this problem, requests arrive in a continuous time online fashion and should be matched to each other. Each request emerges from one out of n sources, with metric inter-source distances. The algorithm is allowed to delay the matching of requests, but with a cost: when matching two requests, it pays the distance between their respective sources and the time each request has waited from its arrival until it was matched. In this paper, we consider the special case of \(n = 2\) sources that captures the essence of the match-or-wait challenge (cf. rent-or-buy). It turns out that even for this degenerate metric space, the problem is far from trivial. Our results include a deterministic 3-competitive online algorithm for this problem, a proof that no deterministic online algorithm can have competitive ratio smaller than 3, and a proof that the same lower bound applies also for the restricted family of memoryless randomized algorithms.

Variable-Version Lovász Local Lemma: Beyond Shearer's Bound

A tight criterion under which the abstract version Lovász Local Lemma (abstract-LLL) holds was given by Shearer [41] decades ago. However, little is known about that of the variable version LLL (variable-LLL) where events are generated by independent random variables, though variable- LLL naturally models and is enough for almost all applications of LLL. We introduce a necessary and sufficient criterion for variable-LLL, in terms of the probabilities of the events and the event-variable graph specifying the dependency among the events. Based on this new criterion, we obtain boundaries for two families of event-variable graphs, namely, cyclic and treelike bigraphs. These are the first two non-trivial cases where the variable-LLL boundary is fully determined. As a byproduct, we also provide a universal constructive method to find a set of events whose union has the maximum probability, given the probability vector and the event-variable graph.Though it is #P-hard in general to determine variable- LLL boundaries, we can to some extent decide whether a gap exists between a variable-LLL boundary and the corresponding abstract-LLL boundary. In particular, we show that the gap existence can be decided without solving Shearer’s conditions or checking our variable-LLL criterion. Equipped with this powerful theorem, we show that there is no gap if the base graph of the event-variable graph is a tree, while gap appears if the base graph has an induced cycle of length at least 4. The problem is almost completely solved except when the base graph has only 3-cliques, in which case we also get partial solutions.A set of reduction rules are established that facilitate to infer gap existence of a event-variable graph from known ones. As an application, various event-variable graphs, in particular combinatorial ones, are shown to be gapful/gapless.

Shortest Paths on Evolving Graphs

We consider the shortest path problem in evolving graphs with restricted access, i.e., the changes are unknown and can be probed only by limited queries. The goal is to maintain a shortest path between a given pair of nodes. We propose a heuristic algorithm that takes into account time-dependent edge reliability and reduces the problem to find an edge-weighted shortest path. Our algorithm leads to higher precision and recall than those of the existing method introduced in [5] on both real-life data and synthetic data, while the error is negligible.

Disentangling the Latent Space of (Variational) Autoencoders for NLP

We train multi-task (variational) autoencoders on linguistic tasks and analyze the learned hidden sentence representations. The representations change significantly when translation and part-of-speech decoders are added. The more decoders are attached, the better the models cluster sentences according to their syntactic similarity, as the representation space becomes less entangled. We compare standard unconstrained autoencoders to variational autoencoders and find significant differences. We achieve better disentanglement with the standard autoencoder, which goes against recent work on variational autoencoders in the visual domain.

Payment Network Design with Fees

Payment channels are the most prominent solution to the blockchain scalability problem. We introduce the problem of network design with fees for payment channels from the perspective of a Payment Service Provider (PSP). Given a set of transactions, we examine the optimal graph structure and fee assignment to maximize the PSP’s profit. A customer prefers to route transactions through the PSP’s network if the cheapest path from sender to receiver is financially interesting, i.e., if the path costs less than the blockchain fee. When the graph structure is a tree, and the PSP facilitates all transactions, the problem can be formulated as a linear program. For a path graph, we present a polynomial time algorithm to assign optimal fees. We also show that the star network, where the center is an additional node acting as an intermediary, is a near-optimal solution to the network design problem.

Minimum cost perfect matching with delays for two sources

Abstract We study a version of the online min-cost perfect matching with delays (MPMD) problem recently introduced by Emek et al. (STOC 2016). In this problem, requests arrive in a continuous time online fashion and should be matched to each other. Each request emerges from one out of n sources, with metric inter-source distances. The algorithm is allowed to delay the matching of requests, but with a cost: when matching two requests, it pays the distance between their respective sources and the time each request has waited from its arrival until it was matched. In this paper, we consider the special case of n = 2 sources that captures the essence of the match-or-wait challenge (cf. rent-or-buy). It turns out that even for this degenerate metric space, the problem is far from trivial. Our results include a deterministic 3-competitive online algorithm for this problem, a proof that no deterministic online algorithm can have competitive ratio smaller than 3, and a proof that the same lower bound applies also for the restricted family of memoryless randomized algorithms.

Communities in Preference Networks: Refined Axioms and Beyond

Borgs et al. [2016] investigated essential requirements for communities in preference networks. They defined six axioms on community functions, i.e., community detection rules. Though having elegant properties, the practicality of this axiomsystem is compromised by the intractability of checking twocritical axioms, so no nontrivial consistent community functionwas reported in [Borgs et al., 2016]. By adapting the two axioms in a natural way, we propose two new axioms that are efficiently-checkable. We show that most of the desirable properties of the original axiom system are preserved. More importantly, the new axioms provide a general approach to constructing consistent community functions. We further find a natural consistent community function that is also enumerable and samplable, answering an open problem in the literature.