Computational Geometry Column 34

Problems presented at the open-problem session of the 14th Annual ACM Symposium on Computational Geometry are listed

RRR: Rank-Regret Representative

Selecting the best items in a dataset is a common task in data exploration. However, the concept of "best" lies in the eyes of the beholder: different users may consider different attributes more important, and hence arrive at different rankings. Nevertheless, one can remove "dominated" items and create a "representative" subset of the data set, comprising the "best items" in it. A Pareto-optimal representative is guaranteed to contain the best item of each possible ranking, but it can be almost as big as the full data. Representative can be found if we relax the requirement to include the best item for every possible user, and instead just limit the users' "regret". Existing work defines regret as the loss in score by limiting consideration to the representative instead of the full data set, for any chosen ranking function. However, the score is often not a meaningful number and users may not understand its absolute value. Sometimes small ranges in score can include large fractions of the data set. In contrast, users do understand the notion of rank ordering. Therefore, alternatively, we consider the position of the items in the ranked list for defining the regret and propose the {\em rank-regret representative} as the minimal subset of the data containing at least one of the top-$k$ of any possible ranking function. This problem is NP-complete. We use the geometric interpretation of items to bound their ranks on ranges of functions and to utilize combinatorial geometry notions for developing effective and efficient approximation algorithms for the problem. Experiments on real datasets demonstrate that we can efficiently find small subsets with small rank-regrets

CHERIvoke: Characterising pointer revocation using CHERI capabilities for temporal memory safety

A lack of temporal safety in low-level languages has led to an epidemic of use-after-free exploits. These have surpassed in number and severity even the infamous buffer-overflow exploits violating spatial safety. Capability addressing can directly enforce spatial safety for the C language by enforcing bounds on pointers and by rendering pointers unforgeable. Nevertheless, an efficient solution for strong temporal memory safety remains elusive. CHERI is an architectural extension to provide hardware capability addressing that is seeing significant commercial and open- source interest. We show that CHERI capabilities can be used as a foundation to enable low-cost heap temporal safety by facilitating out-of-date pointer revocation, as capabilities enable precise and efficient identification and invalidation of pointers, even when using unsafe languages such as C. We develop CHERIvoke, a technique for deterministic and fast sweeping revocation to enforce temporal safety on CHERI systems. CHERIvoke quarantines freed data before periodically using a small shadow map to revoke all dangling pointers in a single sweep of memory, and provides a tunable trade-off between performance and heap growth. We evaluate the performance of such a system using high-performance x86 processors, and further analytically examine its primary overheads. When configured with a heap-size overhead of 25%, we find that CHERIvoke achieves an average execution-time overhead of under 5%, far below the overheads associated with traditional garbage collection, revocation, or page-table systems.EP/K026399/1, EP/P020011/1, EP/K008528/

Cornucopia: Temporal safety for CHERI heaps

Use-after-free violations of temporal memory safety continue to plague software systems, underpinning many high-impact exploits. The CHERI capability system shows great promise in achieving C and C++ language spatial memory safety, preventing out-of-bounds accesses. Enforcing language-level temporal safety on CHERI requires capability revocation, traditionally achieved either via table lookups (avoided for performance in the CHERI design) or by identifying capabilities in memory to revoke them (similar to a garbage-collector sweep). CHERIvoke, a prior feasibility study, suggested that CHERI’s tagged capabilities could make this latter strategy viable, but modeled only architectural limits and did not consider the full implementation or evaluation of the approach. Cornucopia is a lightweight capability revocation system for CHERI that implements non-probabilistic C/C++ temporal memory safety for standard heap allocations. It extends the CheriBSD virtual-memory subsystem to track capability flow through memory and provides a concurrent kernel-resident revocation service that is amenable to multi-processor and hardware acceleration. We demonstrate an average overhead of less than 2% and a worst-case of 8.9% for concurrent revocation on compatible SPEC CPU2006 benchmarks on a multi-core CHERI CPU on FPGA, and we validate Cornucopia against the Juliet test suite’s corpus of temporally unsafe programs. We test its compatibility with a large corpus of C programs by using a revoking allocator as the system allocator while booting multi-user CheriBSD. Cornucopia is a viable strategy for always-on temporal heap memory safety, suitable for production environments.This work was supported by the Defense Advanced Research Projects Agency (DARPA) and the Air Force Research Laboratory (AFRL), under contracts FA8750-10-C-0237 (“CTSRD”) and HR0011-18-C-0016 (“ECATS”). We also acknowledge the EPSRC REMS Programme Grant (EP/K008528/1), the ABP Grant (EP/P020011/1), the ERC ELVER Advanced Grant (789108), the Gates Cambridge Trust, Arm Limited, HP Enterprise, and Google, Inc

New Plane-Sweep Algorithms for Distance-Based Join Queries in Spatial Databases

Efficient and effective processing of the distance-based join query (DJQ) is of great importance in spatial databases due to the wide area of applications that may address such queries (mapping, urban planning, transportation planning, resource management, etc.). The most representative and studied DJQs are the K Closest Pairs Query (KCPQ) and εDistance Join Query (εDJQ). These spatial queries involve two spatial data sets and a distance function to measure the degree of closeness, along with a given number of pairs in the final result (K) or a distance threshold (ε). In this paper, we propose four new plane-sweep-based algorithms for KCPQs and their extensions for εDJQs in the context of spatial databases, without the use of an index for any of the two disk-resident data sets (since, building and using indexes is not always in favor of processing performance). They employ a combination of plane-sweep algorithms and space partitioning techniques to join the data sets. Finally, we present results of an extensive experimental study, that compares the efficiency and effectiveness of the proposed algorithms for KCPQs and εDJQs. This performance study, conducted on medium and big spatial data sets (real and synthetic) validates that the proposed plane-sweep-based algorithms are very promising in terms of both efficient and effective measures, when neither inputs are indexed. Moreover, the best of the new algorithms is experimentally compared to the best algorithm that is based on the R-tree (a widely accepted access method), for KCPQs and εDJQs, using the same data sets. This comparison shows that the new algorithms outperform R-tree based algorithms, in most cases