Finding Optimal Solutions to Token Swapping by Conflict-Based Search and Reduction to SAT

Surynek, Pavel

doi:10.1109/ictai.2018.00096

Cited by 5 publications

(6 citation statements)

References 28 publications

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“…Research around TWP is recent; hence, it has not been as deeply studied as SIP. Among current approaches to solve token swapping, we count two approximative algorithms Yamanaka et al 2017], and an exponential method [Surynek 2018]. Example 2.11 illustrates TWP.…”

Section: Token Swappingmentioning

confidence: 99%

Qubit allocation as a combination of subgraph isomorphism and token swapping

Siraichi

Santos

Collange

et al. 2019

Proc. ACM Program. Lang.

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In 2016, the first quantum processors have been made available to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, such possibility also brought challenges. One challenge is the so called Qubit Allocation problem: the mapping of a virtual quantum circuit into an actual quantum architecture. There exist solutions to this problem; however, in our opinion, they fail to capitalize on decades of improvements on graph theory. In contrast, this paper shows how to model qubit allocation as the combination of Subgraph Isomorphism and Token Swapping. This idea has been made possible by the publication of an approximative solution to the latter problem in 2016. We have compared our algorithm against five other qubit allocators, all independently designed in the last two years, including the winner of the IBM Challenge. When evaluated in łTokyo", a quantum architecture with 20 qubits, our technique outperforms these state-of-the-art approaches in terms of the quality of the solutions that it finds and the amount of memory that it uses, while showing practical runtime. CCS Concepts: • Computer systems organization → Quantum computing; • Software and its engineering → Compilers; • Theory of computation → Parameterized complexity and exact algorithms.

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Section: Token Swappingmentioning

confidence: 99%

Qubit allocation as a combination of subgraph isomorphism and token swapping

Siraichi

Santos

Collange

et al. 2019

Proc. ACM Program. Lang.

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“…Although many works sudying TSWAP from the theoretical point of view exist [2], [9], [25] practical solving of the problem started only lately. In [26] optimal solving of TSWAP by adapted algorithms from MAPF has been suggested. Namely conflict-based search (CBS) [16], [27] and propositional satisfiability-based (SAT) [28] MDD-SAT [17], [18] originally developed for MAPF have been modified for TSWAP.…”

Section: Related Workmentioning

confidence: 99%

“…If a collision (c i , c j , v, t) between tokens c i and c j occurs in v at time step t then we introduce conflicts (c i , v, t) and (c j , v, t) for c i and c j respectively. 4 TSWAP: This problem takes conflicts from TPERM but adds new conflicts that arise from doing something else than swapping [26]. Each time edge {u, v} is being traversed by token c i between time steps t and t + 1, a token residing in v at time step t, that is τ t (v), must go in the opposite direction from v to u.…”

Section: B Adapting Cbs and Mdd-satmentioning

confidence: 99%

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Lazy Modeling of Variants of Token Swapping Problem and Multi-agent Path Finding through Combination of Satisfiability Modulo Theories and Conflict-based Search

Surynek

2018

Preprint

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We address item relocation problems in graphs in this paper. We assume items placed in vertices of an undirected graph with at most one item per vertex. Items can be moved across edges while various constraints depending on the type of relocation problem must be satisfied. We introduce a general problem formulation that encompasses known types of item relocation problems such as multi-agent path finding (MAPF) and token swapping (TSWAP). In this formulation we express two new types of relocation problems derived from token swapping that we call token rotation (TROT) and token permutation (TPERM). Our solving approach for item relocation combines satisfiability modulo theory (SMT) with conflict-based search (CBS). We interpret CBS in the SMT framework where we start with the basic model and refine the model with a collision resolution constraint whenever a collision between items occurs in the current solution. The key difference between the standard CBS and our SMT-based modification of CBS (SMT-CBS) is that the standard CBS branches the search to resolve the collision while in SMT-CBS we iteratively add a single disjunctive collision resolution constraint. Experimental evaluation on several benchmarks shows that the SMT-CBS algorithm significantly outperforms the standard CBS. We also compared SMT-CBS with a modification of the SAT-based MDD-SAT solver that uses an eager modeling of item relocation in which all potential collisions are eliminated by constrains in advance. Experiments show that lazy approach in SMT-CBS produce fewer constraint than MDD-SAT and also achieves faster solving run-times.

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“…Works studying this problem from a theoretical point of view exist [5], [3]; but only a few practical algorithms to solve the problems have very lately been proposed. For example, the author in [6] adapted frameworks used for solving the multi-agent pathfinding problem to solve the token swapping problem and some of its variations.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Algorithms for Token Swapping

Schmitt

Soeken

Micheli

2020

2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL)

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We study different symbolic algorithms to solve two related reconfiguration problems on graphs: the token swapping problem and the permutation routing via matchings problem. Input to both problems is a connected graph with labeled vertices and a token in each vertex. The goal is to move each token to its destination vertex using swap operations. In the token swapping problem, the goal is to find a solution with a minimum number of swaps. In the permutation routing via matchings problem, the goal is to find a solution with a minimum number of steps, where a step is a set of disjoint swaps which can be performed in parallel. First, we present an A* search algorithm. This algorithm can find optimal solutions if used with an admissible heuristic. We also evaluate the use of non-admissible heuristics. In this case, we prove that the result will deviate from an optimum result by at most an even number of swaps. We also present an algorithm based on Boolean satisfiability. We evaluate our methods on a large set of practical benchmarks.

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Finding Optimal Solutions to Token Swapping by Conflict-Based Search and Reduction to SAT

Cited by 5 publications

References 28 publications

Qubit allocation as a combination of subgraph isomorphism and token swapping

Qubit allocation as a combination of subgraph isomorphism and token swapping

Lazy Modeling of Variants of Token Swapping Problem and Multi-agent Path Finding through Combination of Satisfiability Modulo Theories and Conflict-based Search

Symbolic Algorithms for Token Swapping

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