Time-inconsistent behavior, such as procrastination or abandonment of long-term goals, arises when agents evaluate immediate outcomes disproportionately higher than future ones. This leads to globally suboptimal behavior, where plans are frequently revised or abandoned entirely. In the influential model of Kleinberg and Oren (2014) such behavior is modeled by a present-biased agent navigating a task graph toward a goal, making locally optimal decisions at each step based on discounted future costs. As a result, the agent may repeatedly deviate from initially intended plans. Recent work by Belova et al. (2024) introduced a two-agent extension of this model, where a fully-aware principal attempts to guide the present-biased agent through a specific set of critical tasks without causing abandonment. This captures a rich class of principal–agent dynamics in behavioral settings. In this paper, we provide a comprehensive algorithmic characterization of this problem. We analyze its computational complexity through the framework of parameterized algorithms, focusing on graph parameters that naturally emerge in this setting, such as treewidth, vertex cover, and feedback vertex set. Our main result is a fixed-parameter tractable algorithm when parameterized by the treewidth of the task graph and the number of distinct (v,t)-path costs. Our algorithm encaptures several input settings, such as bounded edge costs and restricted task graph structure. We demonstrate that our main result yields efficient algorithms for a number of such configurations. We complement this with tight hardness results, that highlight the extreme difficulty of the problem even on simplest graphs with bounded number of nodes and constant parameter values, and motivate our choice of parameters. We delineate tractable and intractable regions of the problem landscape, which include answers to open questions of Belova et al. (2024).

We present an open-source tool for manipulating Boolean circuits. It implements efficient algorithms, both existing and novel, for a rich variety of frequently used circuit tasks such as satisfiability, synthesis, and minimization. We tested the tool on a wide range of practically relevant circuits (computing, in particular, symmetric and arithmetic functions) that have been optimized intensively by the community for the last three years. The tool helped us to win the IWLS 2024 Programming Contest. In 2023, it was Google DeepMind who took the first place in the competition. We were able to reduce the size of the best circuits from 2023 by 12% on average, whereas for some individual circuits, our size reduction was as large as 83%.

The emergence of high-throughput omics technologies has resulted in their wide application to cancer studies, greatly increasing our understanding of the disruptions occurring at different molecular levels. To fully harness these data, integrative approaches have emerged as essential tools, enabling the combination of multiple omics modalities to uncover disease mechanisms. However, many such approaches overlook gene regulatory mechanisms, which play a central role in the development and progression of cancer. Patient-specific gene regulatory networks (GRNs), representing interactions between regulators (such as transcription factors) and their target genes in each individual tumour, offer a powerful framework to bridge this gap and investigate the regulatory landscape of cancer. In this study, we introduce a novel approach for integrating patient-specific GRNs with multi-omic data and assess whether their inclusion in joint dimensionality reduction models improves survival prediction across multiple cancer types. By applying our method on ten cancer datasets from The Cancer Genome Atlas, we demonstrate that incorporating GRNs enhances associations with patient survival in several cancer types. Focusing on liver cancer, with validation in independent data, our methodology identifies potential mechanisms of gene regulatory dysregulation associated with cancer progression. These were linked to dysregulated fatty acid metabolism, and identified JUND as a potential novel transcriptional regulator driving these processes. Our findings highlight the value of network-based multi-omics integration for uncovering clinically relevant regulatory mechanisms and improving our understanding of cancer biology at the patient-specific level.

The Strong Exponential Time Hypothesis (SETH) asserts that for every \(\varepsilon > 0\) there exists k such that k -SAT requires time \((2-\varepsilon)^{n}\) . The field of fine-grained complexity has leveraged SETH to prove quite tight conditional lower bounds for dozens of problems in various domains and complexity classes, including Edit Distance, Graph Diameter, Hitting Set, Independent Set, and Orthogonal Vectors. Yet, it has been repeatedly asked in the literature whether SETH-hardness results can be proven for other fundamental problems such as Hamiltonian Path, Independent Set, Chromatic Number, MAX- k -SAT, and Set Cover. In this article, we show that fine-grained reductions implying even \(\lambda^{n}\) -hardness of these problems from SETH for any \(\lambda > 1\) , would imply new circuit lower bounds: super-linear lower bounds for Boolean series-parallel circuits or polynomial lower bounds for arithmetic circuits (each of which is a four-decade open question). We also extend this barrier result to the class of parameterized problems. Namely, for every \(\lambda > 1\) we conditionally rule out fine-grained reductions implying SETH-based lower bounds of \(\lambda^{k}\) for a number of problems parameterized by the solution size k . Our main technical tool is a new concept called polynomial formulations. In particular, we show that many problems can be represented by relatively succinct low-degree polynomials, and that any problem with such a representation cannot be proven SETH-hard (without proving new circuit lower bounds).

The present bias is a well-documented behavioral trait that significantly influences human decision-making, with present-biased agents often prioritizing immediate rewards over long-term benefits, leading to suboptimal outcomes in various real-world scenarios. Kleinberg and Oren (2014) proposed a popular graph-theoretical model of inconsistent planning to capture the behavior of present-biased agents. In this model, a multi-step project is represented by a weighted directed acyclic task graph, where the agent traverses the graph based on present-biased preferences. We use the model of Kleinberg and Oren to address the principal-agent problem, where a principal, fully aware of the agent’s present bias, aims to modify an existing project by adding or deleting tasks. The challenge is to create a modified project that satisfies two somewhat contradictory conditions. On one hand, the present-biased agent should select specific tasks deemed important by the principal. On the other hand, if the anticipated costs in the modified project become too high for the agent, there is a risk of the agent abandoning the entire project, which is not in the principal’s interest. To tackle this issue, we leverage the tools of parameterized complexity to investigate whether the principal’s strategy can be efficiently identified. We provide algorithms and complexity bounds for this problem.

More than 40 years ago, Schroeppel and Shamir presented an algorithm that solves the Subset Sum problem for $n$ integers in time $O^*(2^{0.5n})$ and space $O^*(2^{0.25n})$. The time upper bound remains unbeaten, but the space upper bound has been improved to $O^*(2^{0.249999n})$ in a recent breakthrough paper by Nederlof and Węgrzycki (STOC 2021). Their algorithm is a clever combination of a number of previously known techniques with a new reduction and a new algorithm for the Orthogonal Vectors problem. In this paper, we improve the space bound by Nederlof and Węgrzycki to $O^*(2^{0.246n})$ and also simplify their algorithm and its analysis. We achieve this by using an idea, due to Howgrave-Graham and Joux, of using a random prime number to filter the family of subsets. We incorporate it into the algorithm by Schroeppel and Shamir and then use this amalgam inside the representation technique. This allows us to reduce an instance of Subset Sum to a larger number of instances of weighted orthogonal vector.

The field of fine-grained complexity aims at proving conditional lower bounds on the time complexity of computational problems. One of the most popular and successfully used assumptions, Strong Exponential Time Hypothesis (SETH), implies that SAT cannot be solved in 2(1-ɛ)n time. In recent years, it has been proved that known algorithms for many problems are optimal under SETH. Despite the wide applicability of SETH, for many problems, there are no known SETH-based lower bounds, so the quest for new reductions continues.

The Strong Exponential Time Hypothesis (SETH) asserts that for every ε > 0 there exists k such that k-SAT requires time (2 — ε)n. The field of fine-grained complexity has leveraged SETH to prove quite tight conditional lower bounds for dozens of problems in various domains and complexity classes, including Edit Distance, Graph Diameter, Hitting Set, Independent Set, and Orthogonal Vectors. Yet, it has been repeatedly asked in the literature whether SETH-hardness results can be proven for other fundamental problems such as Hamiltonian Path, Independent Set, Chromatic Number, MAX-k-SAT, and Set Cover. In this paper, we show that fine-grained reductions implying even λn-hardness of these problems from SETH for any λ > 1, would imply new circuit lower bounds: super-linear lower bounds for Boolean series-parallel circuits or polynomial lower bounds for arithmetic circuits (each of which is a four-decade open question). We also extend this barrier result to the class of parameterized problems. Namely, for every λ > 1, we conditionally rule out fine-grained reductions implying SETH-based lower bounds of λk: for a number of problems parameterized by the solution size k. Our main technical tool is a new concept called polynomial formulations. In particular, we show that many problems can be represented by relatively succinct low-degree polynomials, and that any problem with such a representation cannot be proven SETH-hard (without proving new circuit lower bounds). * The full version of the paper can be accessed at https://arxiv.org/abs/2205.07709