arXiv subjects

Joseph Poremba

Publications and source records attributed to Joseph Poremba.

3 recordsLinked to original sources

arXiv2025

Uncrossed Multiflows and Applications to Disjoint Paths

A multiflow in a planar graph is uncrossed if its support paths do not cross. Recently such flows have played a role in approximation algorithms for maximum disjoint paths in "fully-planar" instances, where the combined supply-demand graph is planar, as well as low-congestion unsplittable flows for fully-planar and single-source instances. We investigate the utility of uncrossed flow more generally and ask three key questions. First, are there other interesting planar multiflow instances that admit uncrossed flows? We answer affirmatively, demonstrating a new family of "pairwise-planar" instances whose flows can be uncrossed. This family subsumes fully-planar but includes substantially more, such as fully-compliant series-parallel instances and some instances that have large clique demand graphs. Second, can we always round a fractional uncrossed flow to a "good" integral flow? We again answer positively. For maximization problems, we obtain integral flows with a constant fraction of the original value. For congestion problems (where we fully route all given demands), we obtain integral flows with edge congestion 2. Consequently, we obtain constant-factor approximation algorithms for maximum disjoint paths and minimum congestion integer multiflow for pairwise-planar instances, and show such instances have a constant integral flow-multicut gap. Finally, given a planar multiflow instance, can we determine if there exists a congestion-1 uncrossed fractional flow (congestion) or find the maximum value uncrossed fractional flow (maximization)? For congestion, we show this problem is NP-hard, but finding uncrossed edge-disjoint paths is polytime solvable if the demands span a bounded number of faces. For maximization, we present a strong inapproximability result.

cs.DS↗

arXiv2024

Portus: Linking Alloy with SMT-based Finite Model Finding

Alloy is a well-known, formal, declarative language for modelling systems early in the software development process. Currently, it uses the Kodkod library as a back-end for finite model finding. Kodkod translates the model to a SAT problem; however, this method can often handle only problems of fairly low-size sets and is inherently finite. We present Portus, a method for translating Alloy into an equivalent many-sorted first-order logic problem (MSFOL). Once in MSFOL, the problem can be evaluated by an SMT-based finite model finding method implemented in the Fortress library, creating an alternative back-end for the Alloy Analyzer. Fortress converts the MSFOL finite model finding problem into the logic of uninterpreted functions with equality (EUF), a decidable fragment of first-order logic that is well-supported in many SMT solvers. We compare the performance of Portus with Kodkod on a corpus of 63 Alloy models written by experts. Our method is fully integrated into the Alloy Analyzer.

cs.SE↗

arXiv2020

Static Symmetry Breaking in Many-Sorted Finite Model Finding

Symmetry in finite model finding problems of many-sorted first-order logic (MSFOL) can be exploited to reduce the number of interpretations considered during search, thereby improving solver performance. In this thesis, we situate symmetry of many-sorted finite model finding (MSFMF) problems in a general framework used for constraint satisfaction problems (CSP). We survey and classify existing approaches to symmetry for MSFOL as used in tools such as Paradox. We provide new insight into how sorts affect the existence of symmetry and how sort inference can be viewed as a symmetry detection mechanism. Finally, we present two new symmetry breaking schemes for MSFOL that are implemented at the MSFOL level and discuss when schemes can be combined. We prove the correctness of our new methods.

cs.LO↗