Dynamic Dominators and Low-High Orders in DAGs

We consider practical algorithms for maintaining the dominator tree and a low-high order in directed acyclic graphs (DAGs) subject to dynamic operations. Let G be a directed graph with a distinguished start vertex s. The dominator tree D of G is a tree rooted at s, such that a vertex v is an ancestor of a vertex w if and only if all paths from s to w in G include v. The dominator tree is a central tool in program optimization and code generation, and has many applications in other diverse areas including constraint programming, circuit testing, biology, and in algorithms for graph connectivity problems. A low-high order of G is a preorder of D that certifies the correctness of D, and has further applications in connectivity and path-determination problems. We first provide a practical and carefully engineered version of a recent algorithm [ICALP 2017] for maintaining the dominator tree of a DAG through a sequence of edge deletions. The algorithm runs in O(mn) total time and O(m) space, where n is the number of vertices and m is the number of edges before any deletion. In addition, we present a new algorithm that maintains a low-high order of a DAG under edge deletions within the same bounds. Both results extend to the case of reducible graphs (a class that includes DAGs). Furthermore, we present a fully dynamic algorithm for maintaining the dominator tree of a DAG under an intermixed sequence of edge insertions and deletions. Although it does not maintain the O(mn) worst-case bound of the decremental algorithm, our experiments highlight that the fully dynamic algorithm performs very well in practice. Finally, we study the practical efficiency of all our algorithms by conducting an extensive experimental study on real-world and synthetic graphs

Adaptive Constraint Solving for Information Flow Analysis

In program analysis, unknown properties for terms are typically represented symbolically as variables. Bound constraints on these variables can then specify multiple optimisation goals for computer programs and nd application in areas such as type theory, security, alias analysis and resource reasoning. Resolution of bound constraints is a problem steeped in graph theory; interdependencies between the variables is represented as a constraint graph. Additionally, constants are introduced into the system as concrete bounds over these variables and constants themselves are ordered over a lattice which is, once again, represented as a graph. Despite graph algorithms being central to bound constraint solving, most approaches to program optimisation that use bound constraint solving have treated their graph theoretic foundations as a black box. Little has been done to investigate the computational costs or design e cient graph algorithms for constraint resolution. Emerging examples of these lattices and bound constraint graphs, particularly from the domain of language-based security, are showing that these graphs and lattices are structurally diverse and could be arbitrarily large. Therefore, there is a pressing need to investigate the graph theoretic foundations of bound constraint solving. In this thesis, we investigate the computational costs of bound constraint solving from a graph theoretic perspective for Information Flow Analysis (IFA); IFA is a sub- eld of language-based security which veri es whether con dentiality and integrity of classified information is preserved as it is manipulated by a program. We present a novel framework based on graph decomposition for solving the (atomic) bound constraint problem for IFA. Our approach enables us to abstract away from connections between individual vertices to those between sets of vertices in both the constraint graph and an accompanying security lattice which defines ordering over constants. Thereby, we are able to achieve significant speedups compared to state-of-the-art graph algorithms applied to bound constraint solving. More importantly, our algorithms are highly adaptive in nature and seamlessly adapt to the structure of the constraint graph and the lattice. The computational costs of our approach is a function of the latent scope of decomposition in the constraint graph and the lattice; therefore, we enjoy the fastest runtime for every point in the structure-spectrum of these graphs and lattices. While the techniques in this dissertation are developed with IFA in mind, they can be extended to other application of the bound constraints problem, such as type inference and program analysis frameworks which use annotated type systems, where constants are ordered over a lattice

Advances in Functional Decomposition: Theory and Applications

Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing. This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient. The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering. The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time. The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function. The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches. Finally we present two publications that resulted from the many detours we have taken along the winding path of our research

Processor Models For Instruction Scheduling using Constraint Programming

Instruction scheduling is one of the most important optimisations performed when producing code in a compiler. The problem consists of finding a minimum length schedule subject to latency and different resource constraints. This is a hard problem, classically approached by heuristic algorithms. In the last decade, research interest has shifted from heuristic to potentially optimal methods. When using optimal methods, a lot of compilation time is spent searching for an optimal solution. This makes it important that the problem definition reflects the reality of the processor. In this work, a constraint programming approach was used to study the impact that the model detail has on performance. Several models of a superscalar processor were embedded in LLVM and evaluated using SPEC CPU2000. The result shows that there is substantial performance to be gained, over 5% for some programs. The stability of the improvement is heavily dependent on the accuracy of the model

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Graph-theoretic Properties of Control Flow Graphs and Applications

This thesis deals with determining appropriate width parameters of control flow graphs so that certain computationally hard problems of practical interest become efficiently solvable. A well-known result of Thorup states that the treewidth of control flow graphs arising from structured (goto-free) programs is at most six. However, since a control flow graph is inherently directed, it is very likely that using a digraph width measure would give better algorithms for problems where directional properties of edges are important. One such problem, parity game, is closely related to the μ-calculus model checking problem in software verification and is known to be tractable on graphs of bounded DAG-width, Kelly-width or entanglement. Motivated by this, we show that the DAG-width of control flow graphs arising from structured programs is at most three and give a linear-time algorithm to compute the corresponding DAG decomposition. Using similar techniques, we show that Kelly-width of control flow graphs is also bounded by three. Additionally, we also show that control flow graphs can have unbounded entanglement. In light of these results, we revisit the complexity of the μ-calculus model checking problem on these special graph classes and show that we can obtain better running times for control flow graphs

Sparsity-aware neural user behavior modeling in online interaction platforms

Modern online platforms offer users an opportunity to participate in a variety of content-creation, social networking, and shopping activities. With the rapid proliferation of such online services, learning data-driven user behavior models is indispensable to enable personalized user experiences. Recently, representation learning has emerged as an effective strategy for user modeling, powered by neural networks trained over large volumes of interaction data. Despite their enormous potential, we encounter the unique challenge of data sparsity for a vast majority of entities, e.g., sparsity in ground-truth labels for entities and in entity-level interactions (cold-start users, items in the long-tail, and ephemeral groups). In this dissertation, we develop generalizable neural representation learning frameworks for user behavior modeling designed to address different sparsity challenges across applications. Our problem settings span transductive and inductive learning scenarios, where transductive learning models entities seen during training and inductive learning targets entities that are only observed during inference. We leverage different facets of information reflecting user behavior (e.g., interconnectivity in social networks, temporal and attributed interaction information) to enable personalized inference at scale. Our proposed models are complementary to concurrent advances in neural architectural choices and are adaptive to the rapid addition of new applications in online platforms. First, we examine two transductive learning settings: inference and recommendation in graph-structured and bipartite user-item interactions. In chapter 3, we formulate user profiling in social platforms as semi-supervised learning over graphs given sparse ground-truth labels for node attributes. We present a graph neural network framework that exploits higher-order connectivity structures (network motifs) to learn attributed structural roles of nodes that identify structurally similar nodes with co-varying local attributes. In chapter 4, we design neural collaborative filtering models for few-shot recommendations over user-item interactions. To address item interaction sparsity due to heavy-tailed distributions, our proposed meta-learning framework learns-to-recommend few-shot items by knowledge transfer from arbitrary base recommenders. We show that our framework consistently outperforms state-of-art approaches on overall recommendation (by 5% Recall) while achieving significant gains (of 60-80% Recall) for tail items with fewer than 20 interactions. Next, we explored three inductive learning settings: modeling spread of user-generated content in social networks; item recommendations for ephemeral groups; and friend ranking in large-scale social platforms. In chapter 5, we focus on diffusion prediction in social networks where a vast population of users rarely post content. We introduce a deep generative modeling framework that models users as probability distributions in the latent space with variational priors parameterized by graph neural networks. Our approach enables massive performance gains (over 150% recall) for users with sparse activities while being faster than state-of-the-art neural models by an order of magnitude. In chapter 6, we examine item recommendations for ephemeral groups with limited or no historical interactions together. To overcome group interaction sparsity, we present self-supervised learning strategies that exploit the preference co-variance in observed group memberships for group recommender training. Our framework achieves significant performance gains (over 30% NDCG) over prior state-of-the-art group recommendation models. In chapter 7, we introduce multi-modal inference with graph neural networks that captures knowledge from multiple feature modalities and user interactions for multi-faceted friend ranking. Our approach achieves notable higher performance gains for critical populations of less-active and low degree users

Beta-Conversion, Efficiently

Type-checking in dependent type theories relies on conversion, i.e. testing given lambda-terms for equality up to beta-evaluation and alpha-renaming. Computer tools based on the lambda-calculus currently implement conversion by means of algorithms whose complexity has not been identified, and in some cases even subject to an exponential time overhead with respect to the natural cost models (number of evaluation steps and size of input lambda-terms). This dissertation shows that in the pure lambda-calculus it is possible to obtain conversion algorithms with bilinear time complexity when evaluation is carried following evaluation strategies that generalize Call-by-Value to the stronger case required by conversion

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum