The Dancing problem requires a swarm of n autonomous mobile robots to form a sequence of patterns, aka perform a choreography. Existing work has proven that some crucial restrictions on choreographies and initial configurations (e.g., on repetitions of patterns, periodicity, symmetries, contractions/expansions) must hold so that the Dancing problem can be solved under certain robot models. Here, we prove that these necessary constraints can be dropped by considering the LUMI model (i.e., where robots are endowed with a light whose color can be chosen from a constant-size palette) under the quite unexplored sequential scheduler. We formalize the class of Universal Dancing problems which require a swarm of n robots starting from any initial configuration to perform a (periodic or finite) sequence of arbitrary patterns, only provided that each pattern consists of n vertices (including multiplicities). However, we prove that, to be solvable under LUMI, the length of the feasible choreographies is bounded by the compositions of n into the number of colors available to the robots. We provide an algorithm solving the Universal Dancing problem by exploiting the peculiar capability of sequential robots to implement a distributed counter mechanism. Even assuming non-rigid movements, our algorithm ensures spatial homogeneity of the performed choreography.
In this paper, we resolve a long-standing open problem in self-stabilization asking whether it is possible to construct a spanning tree using constant memory per node in a synchronous semi-uniform networks, i.e., networks in which one node is distinguished. We design a synchronous self-stabilizing algorithm that constructs a breadth-first search (BFS) tree in any anonymous semi-uniform network using only a constant number of bits of memory per node. Crucially, our approach operates without any prior knowledge of global network parameters such as maximum degree, diameter, or number of nodes. In contrast to traditional self-stabilizing methods - such as pointer-to-neighbors, distance-toroot, or identifiers - that are unsuitable under strict memory constraints, our solution employs an innovative constant-space token dissemination mechanism. This mechanism effectively eliminates cycles and rectifies errors in the BFS structure, ensuring both correctness and memory efficiency. The proposed algorithm not only meets the stringent requirements of memory-constrained distributed systems, but also opens new avenues for research in the design of self-stabilizing protocols under severe resource limitations: constant space-complexity may not systematically prevent the existence of self-stabilizing algorithms for important non-trivial tasks. 2012 ACM Subject Classification Theory of computation -> Design and analysis of algorithms; Mathematics of computing -> Discrete mathematics
In protocols with asymmetric trust, each participant is free to make its own trust assumptions about others, captured by an asymmetric quorum system. This contrasts with ordinary, symmetric quorum systems and threshold models, where trust assumptions are uniformly shared among participants. Fundamental problems like reliable broadcast and consensus are unsolvable in the asymmetric model if quorum systems satisfy only the classical properties of consistency and availability. As a result, existing solutions introduce stronger assumptions to circumvent this limitation. We show that some requirements used by state-of-the-art approaches are overly restrictive, so much so that they effectively eliminate the benefits of asymmetric trust. To address this, we propose a new approach to characterize asymmetric problems and, building upon it, present an asymmetric asynchronous unauthenticated reliable broadcast algorithm that significantly weakens the assumptions needed to solve the problem. Our techniques are general and can be readily adapted to other core problems in the asymmetric trust setting. 2012 ACM Subject Classification Theory of computation -> Distributed algorithms
We study the exploration problem by mobile agents in Connectivity Time dynamic graphs. The Connectivity Time model was introduced by Michail et al. [JPDC 2014] and is arguably one of the weakest dynamic graph connectivity models. We prove that exploration is impossible in such graphs using ( n-1)( n-2)/2 mobile agents starting from an arbitrary initial configuration, even when agents have full knowledge of system parameters, global communication, full visibility, and infinite memory. We then present an exploration algorithm that uses ( n-1)( n-2)/2 + 1 agents equipped with global communication, 1-hop visibility and O(log n) memory. 2012 ACM Subject Classification Theory of computation -> Distributed algorithms
Total Store Order (TSO) is one of the most popular relaxed memory model in multiprocessor architectures, widely implemented, for example, in Intel's x86 and x64 platforms. It delays write visibility via store buffers, thereby allowing a significant improvement in efficiency. This, however, complicates reasoning about correctness, as executions may violate sequential consistency. We present a semantic framework that provides effective tools that can pinpoint when such synchronization is necessary under TSO. We define a TSO-specific occurs -before relation, adapting Lamport's happens-before to TSO, and prove that events at different sites can be temporally ordered only via an occurs-before chain. Analyzing how fences and RMW5 create these chains lets us identify when they are unavoidable. We present in this BA how these results impact linearizable implementations of registers, capturing information flow and causality in TSO. The full version of this work provides details as well as results regarding the need for synchronization in linearizable implementations of additional objects.
