Spread and defend infection in graphs

The spread of an infection, a contagion, meme, emotion, message and various other spreadable objects have been discussed in several works. Burning and firefighting have been discussed in particular on static graphs. Graph burning simulates the notion of the spread of "fire" throughout a graph (plus, one unburned node burned at each time-step); graph firefighting simulates the defending of nodes by placing firefighters on the nodes which have not been already burned while the fire is being spread (started by only a single fire source). This article studies a combination of firefighting and burning on a graph class which is a variation (generalization) of temporal graphs. Nodes can be infected from "outside" a network. We present a notion of both upgrading (of unburned nodes, similar to firefighting) and repairing (of infected nodes). The nodes which are burned, firefighted, or repaired are chosen probabilistically. So a variable amount of nodes are allowed to be infected, upgraded and repaired in each time step. In the model presented in this article, both burning and firefighting proceed concurrently, we introduce such a system to enable the community to study the notion of spread of an infection and the notion of upgrade/repair against each other. The graph class that we study (on which, these processes are simulated) is a variation of temporal graph class in which at each time-step, probabilistically, a communication takes place (iff an edge exists in that time step). In addition, a node can be "worn out" and thus can be removed from the network, and a new healthy node can be added to the network as well. This class of graphs enables systems with high complexity to be able to be simulated and studied

Multiplication and Modulo are Lattice Linear

In this paper, we analyze lattice linearity of multiplication and modulo operations. We demonstrate that these operations are lattice linear and the parallel processing algorithms that we study for both these operations are able to exploit the lattice linearity of their respective problems. This implies that these algorithms can be implemented in asynchronous environments, where the nodes are allowed to read old information from each other and are still guaranteed to converge within the same time complexity. These algorithms also exhibit properties similar to snap-stabilization, i.e., starting from an arbitrary state, the system follows the trace strictly according to its specification

Lattice Linear Problems vs Algorithms

Modelling problems using predicates that induce a partial order among global states was introduced as a way to permit asynchronous execution in multiprocessor systems. A key property of such problems is that the predicate induces one lattice in the state space which guarantees that the execution is correct even if nodes execute with old information about their neighbours. Thus, a compiler that is aware of this property can ignore data dependencies and allow the application to continue its execution with the available data rather than waiting for the most recent one. Unfortunately, many interesting problems do not exhibit lattice linearity. This issue was alleviated with the introduction of eventually lattice linear algorithms. Such algorithms induce a partial order in a subset of the state space even though the problem cannot be defined by a predicate under which the states form a partial order. This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It also introduces a new class of algorithms called (fully) lattice linear algorithms. A characteristic of these algorithms is that the entire reachable state space is partitioned into one or more lattices and the initial state locks into one of these lattices. Thus, under a few additional constraints, the initial state can uniquely determine the final state. For demonstration, we present lattice linear self-stabilizing algorithms for minimal dominating set and graph colouring problems, and a parallel processing 2-approximation algorithm for vertex cover. The algorithm for minimal dominating set converges in n moves, and that for graph colouring converges in n+2m moves. The algorithm for vertex cover is the first lattice linear approximation algorithm for an NP-Hard problem; it converges in n moves. Some part is cut due to 1920 character limit. Please see the pdf for full abstract.Comment: arXiv admin note: text overlap with arXiv:2209.1470

Lattice Linearity in Assembling Myopic Robots on an Infinite Triangular Grid

In this paper, we study the problem of gathering distance-1 myopic robots on an infinite triangular grid. We show that the algorithm developed by Goswami et al. (SSS, 2022) is lattice linear. This implies that a distributed scheduler, assumed therein, is not required for this algorithm: it runs correctly in asynchrony. It also implies that the algorithm works correctly even if the robots are equipped with a unidirectional \textit{camera} to see the neighbouring robots (rather than an omnidirectional one, which would be required under a distributed scheduler). Due to lattice linearity, we can predetermine the point of gathering. We also show that this algorithm converges in $2n$ rounds, which is lower than that ($2.5(n+1)$ rounds) shown in Goswami et al.Comment: arXiv admin note: text overlap with arXiv:2302.0720

Technical Report: Using Static Analysis to Compute Benefit of Tolerating Consistency

Synchronization is the Achilles heel of concurrent programs. Synchronization requirement is often used to ensure that the execution of the concurrent program can be serialized. Without synchronization requirement, a program suffers from consistency violations. Recently, it was shown that if programs are designed to tolerate such consistency violation faults (\cvf{s}) then one can obtain substantial performance gain. Previous efforts to analyze the effect of \cvf-tolerance are limited to run-time analysis of the program to determine if tolerating \cvf{s} can improve the performance. Such run-time analysis is very expensive and provides limited insight. In this work, we consider the question, `Can static analysis of the program predict the benefit of \cvf-tolerance?' We find that the answer to this question is affirmative. Specifically, we use static analysis to evaluate the cost of a \cvf and demonstrate that it can be used to predict the benefit of \cvf-tolerance. We also find that when faced with a large state space, partial analysis of the state space (via sampling) also provides the required information to predict the benefit of \cvf-tolerance. Furthermore, we observe that the \cvf-cost distribution is exponential in nature, i.e., the probability that a \cvf has a cost of $c$ is $A.B^{-c}$, where $A$ and $B$ are constants, i.e., most \cvf{s} cause no/low perturbation whereas a small number of \cvf{s} cause a large perturbation. This opens up new aveneus to evaluate the benefit of \cvf-tolerance

Evaluation of a quality improvement intervention to reduce anastomotic leak following right colectomy (EAGLE): pragmatic, batched stepped-wedge, cluster-randomized trial in 64 countries

Background Anastomotic leak affects 8 per cent of patients after right colectomy with a 10-fold increased risk of postoperative death. The EAGLE study aimed to develop and test whether an international, standardized quality improvement intervention could reduce anastomotic leaks. Methods The internationally intended protocol, iteratively co-developed by a multistage Delphi process, comprised an online educational module introducing risk stratification, an intraoperative checklist, and harmonized surgical techniques. Clusters (hospital teams) were randomized to one of three arms with varied sequences of intervention/data collection by a derived stepped-wedge batch design (at least 18 hospital teams per batch). Patients were blinded to the study allocation. Low- and middle-income country enrolment was encouraged. The primary outcome (assessed by intention to treat) was anastomotic leak rate, and subgroup analyses by module completion (at least 80 per cent of surgeons, high engagement; less than 50 per cent, low engagement) were preplanned. Results A total 355 hospital teams registered, with 332 from 64 countries (39.2 per cent low and middle income) included in the final analysis. The online modules were completed by half of the surgeons (2143 of 4411). The primary analysis included 3039 of the 3268 patients recruited (206 patients had no anastomosis and 23 were lost to follow-up), with anastomotic leaks arising before and after the intervention in 10.1 and 9.6 per cent respectively (adjusted OR 0.87, 95 per cent c.i. 0.59 to 1.30; P = 0.498). The proportion of surgeons completing the educational modules was an influence: the leak rate decreased from 12.2 per cent (61 of 500) before intervention to 5.1 per cent (24 of 473) after intervention in high-engagement centres (adjusted OR 0.36, 0.20 to 0.64; P < 0.001), but this was not observed in low-engagement hospitals (8.3 per cent (59 of 714) and 13.8 per cent (61 of 443) respectively; adjusted OR 2.09, 1.31 to 3.31). Conclusion Completion of globally available digital training by engaged teams can alter anastomotic leak rates. Registration number: NCT04270721 (http://www.clinicaltrials.gov)