arXiv subjects

Philipp Woelfel

Publications and source records attributed to Philipp Woelfel.

17 recordsLinked to original sources

arXiv2026

Efficient Randomized LL/SC that Preserves History Independence

We study the fundamental problem of implementing $m$ linearizable LL/SC objects with constant expected step complexity in a system of $n$ processes, using bounded base objects commonly available in hardware. Assuming that each process may have at most $\tau$ outstanding LL() operations, the best known deterministic algorithm requires $\Omega(n^2\tau + m)$ base objects (CAS and registers) [Blelloch and Wei, DISC 2020]. Previously, no comparable randomized algorithm was known. By employing randomization and FADD in addition to CAS and registers, we obtain a space bound of $O(n\tau+m)$ against the weak adaptive adversary. For $m=O(1)$ this matches a lower bound for algorithms using CAS and registers [Aghazadeh and Woelfel, PODC 2015]. In addition, our object can be employed by quiescently history-independent (QHI) algorithms: Whenever no operation on the object is pending and no process has an outstanding LL() operation, its internal memory state is uniquely determined by the values of the $m$ LL/SC objects. An important application is a recent QHI dynamic hashing algorithm, which uses $\Theta(m)$ hardware LL/SC objects to maintain a hash table of size $m$ [Attiya, Bender, Farach-Colton, Oshman, and Schiller, STOC 2025]. But LL/SC is not available in hardware, and prior to our work no wait-free or efficient lock-free software implementation of LL/SC with similar properties was known. Our work demonstrates that one can actually implement the hashing algorithm on available hardware, without an asymptotic increase in step and space complexity, under the reasonable assumption that $m=\Omega(n)$.

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arXiv2021

Tight Lower Bounds for the RMR Complexity of Recoverable Mutual Exclusion

We present a tight RMR complexity lower bound for the recoverable mutual exclusion (RME) problem, defined by Golab and Ramaraju \cite{GR2019a}. In particular, we show that any $n$-process RME algorithm using only atomic read, write, fetch-and-store, fetch-and-increment, and compare-and-swap operations, has an RMR complexity of $Ω(\log n/\log\log n)$ on the CC and DSM model. This lower bound covers all realistic synchronization primitives that have been used in RME algorithms and matches the best upper bounds of algorithms employing swap objects (e.g., [5,6,10]). Algorithms with better RMR complexity than that have only been obtained by either (i) assuming that all failures are system-wide [7], (ii) employing fetch-and-add objects of size $(\log n)^{ω(1)}$ [12], or (iii) using artificially defined synchronization primitives that are not available in actual systems [6,9].

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arXiv2019

Strongly Linearizable Implementations of Snapshots and Other Types

Linearizability is the gold standard of correctness conditions for shared memory algorithms, and historically has been considered the practical equivalent of atomicity. However, it has been shown [1] that replacing atomic objects with linearizable implementations can affect the probability distribution of execution outcomes in randomized algorithms. Thus, linearizable objects are not always suitable replacements for atomic objects. A stricter correctness condition called strong linearizability has been developed and shown to be appropriate for randomized algorithms in a strong adaptive adversary model [1]. We devise several new lock-free strongly linearizable implementations from atomic registers. In particular, we give the first strongly linearizable lock-free snapshot implementation that uses bounded space. This improves on the unbounded space solution of Denysyuk and Woelfel [2]. As a building block, our algorithm uses a lock-free strongly linearizable ABA-detecting register. We obtain this object by modifying the wait-free linearizable ABA-detecting register of Aghazadeh and Woelfel [3], which, as we show, is not strongly linearizable. Aspnes and Herlihy [4] identified a wide class types that have wait-free linearizable implementations from atomic registers. These types require that any pair of operations either commute, or one overwrites the other. Aspnes and Herlihy gave a general wait-free linearizable implementation of such types, employing a wait-free linearizable snapshot object. Replacing that snapshot object with our lock-free strongly linearizable one, we prove that all types in this class have a lock-free strongly linearizable implementation from atomic registers.

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arXiv2019

Efficient Randomized Test-And-Set Implementations

We study randomized test-and-set (TAS) implementations from registers in the asynchronous shared memory model with n processes. We introduce the problem of group election, a natural variant of leader election, and propose a framework for the implementation of TAS objects from group election objects. We then present two group election algorithms, each yielding an efficient TAS implementation. The first implementation has expected max-step complexity $O(\log^\ast k)$ in the location-oblivious adversary model, and the second has expected max-step complexity $O(\log\log k)$ against any read/write-oblivious adversary, where $k\leq n$ is the contention. These algorithms improve the previous upper bound by Alistarh and Aspnes [2] of $O(\log\log n)$ expected max-step complexity in the oblivious adversary model. We also propose a modification to a TAS algorithm by Alistarh, Attiya, Gilbert, Giurgiu, and Guerraoui [5] for the strong adaptive adversary, which improves its space complexity from super-linear to linear, while maintaining its $O(\log n)$ expected max-step complexity. We then describe how this algorithm can be combined with any randomized TAS algorithm that has expected max-step complexity $T(n)$ in a weaker adversary model, so that the resulting algorithm has $O(\log n)$ expected max-step complexity against any strong adaptive adversary and $O(T(n))$ in the weaker adversary model. Finally, we prove that for any randomized 2-process TAS algorithm, there exists a schedule determined by an oblivious adversary such that with probability at least $(1/4)^t$ one of the processes needs at least t steps to finish its TAS operation. This complements a lower bound by Attiya and Censor-Hillel [7] on a similar problem for $n\geq 3$ processes.

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arXiv2018

Optimal Memory-Anonymous Symmetric Deadlock-Free Mutual Exclusion

The notion of an anonymous shared memory (recently introduced in PODC 2017) considers that processes use different names for the same memory location. Hence, there is permanent disagreement on the location names among processes. In this context, the PODC paper presented -among other results- a symmetric deadlock-free mutual exclusion (mutex) algorithm for two processes and a necessary condition on the size $m$ of the anonymous memory for the existence of a symmetric deadlock-free mutex algorithm in an $n$-process system. This condition states that $m$ must be greater than $1$ and belong to the set $M(n)=\{m:\forall~\ell:1<\ell\leq n:~\gcd(\ell,m)=1\}$ (symmetric means that, while each process has its own identity, process identities can only be compared with equality). The present paper answers several open problems related to symmetric deadlock-free mutual exclusion in an $n$-process system ($n\geq 2$) where the processes communicate through $m$ registers. It first presents two algorithms. The first considers that the registers are anonymous read/write atomic registers and works for any $m$ greater than $1$ and belonging to the set $M(n)$. It thus shows that this condition on $m$ is both necessary and sufficient. The second algorithm considers anonymous read/modify/write atomic registers. It assumes that $m\in M(n)$. These algorithms differ in their design principles and their costs (measured as the number of registers which must contain the identity of a process to allow it to enter the critical section). The paper also shows that the condition $m\in M(n)$ is necessary for deadlock-free mutex on top of anonymous read/modify/write atomic registers. It follows that, when $m>1$, $m\in M(n)$ is a tight characterization of the size of the anonymous shared memory needed to solve deadlock-free mutex, be the anonymous registers read/write or read/modify/write.

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arXiv2018

An Almost Tight RMR Lower Bound for Abortable Test-And-Set

We prove a lower bound of Omega(log n/loglog n) for the remote memory reference (RMR) complexity of abortable test-and-set (leader election) in the cache-coherent (CC) and the distributed shared memory (DSM) model. This separates the complexities of abortable and non-abortable test-and-set, as the latter has constant RMR complexity (Golab, Hendler, Woelfel, SIAM Journal of Computing Vol. 39, 2010). Golab, Hendler, Hadzilacos and Woelfel (Distributed Computing Vol. 25, 2012) showed that compare-and-swap can be implemented from registers and TAS objects with constant RMR complexity. We observe that a small modification to that implementation is abortable, provided that the used TAS objects are abortable.

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arXiv2016

A Simple Hash Class with Strong Randomness Properties in Graphs and Hypergraphs

We study randomness properties of graphs and hypergraphs generated by simple hash functions. Several hashing applications can be analyzed by studying the structure of $d$-uniform random ($d$-partite) hypergraphs obtained from a set $S$ of $n$ keys and $d$ randomly chosen hash functions $h_1,\dots,h_d$ by associating each key $x\in S$ with a hyperedge $\{h_1(x),\dots, h_d(x)\}$. Often it is assumed that $h_1,\dots,h_d$ exhibit a high degree of independence. We present a simple construction of a hash class whose hash functions have small constant evaluation time and can be stored in sublinear space. We devise general techniques to analyze the randomness properties of the graphs and hypergraphs generated by these hash functions, and we show that they can replace other, less efficient constructions in cuckoo hashing (with and without stash), the simulation of a uniform hash function, the construction of a perfect hash function, generalized cuckoo hashing and different load balancing scenarios.

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arXiv2016

Deterministic and Fast Randomized Test-and-Set in Optimal Space

The test-and-set object is a fundamental synchronization primitive for shared memory systems. A test-and-set object stores a bit, initialized to 0, and supports one operation, test&set(), which sets the bit's value to 1 and returns its previous value. This paper studies the number of atomic registers required to implement a test-and-set object in the standard asynchronous shared memory model with n processes. The best lower bound is log(n)-1 for obstruction-free (Giakkoupis and Woelfel, 2012) and deadlock-free (Styer and Peterson, 1989) implementations. Recently a deterministic obstruction-free implementation using O(sqrt(n)) registers was presented (Giakkoupis, Helmi, Higham, and Woelfel, 2013). This paper closes the gap between these known upper and lower bounds by presenting a deterministic obstruction-free implementation of a test-and-set object from Theta(log n) registers of size Theta(log n) bits. We also provide a technique to transform any deterministic obstruction-free algorithm, in which, from any configuration, any process can finish if it runs for b steps without interference, into a randomized wait-free algorithm for the oblivious adversary, in which the expected step complexity is polynomial in n and b. This transformation allows us to combine our obstruction-free algorithm with the randomized test-and-set algorithm by Giakkoupis and Woelfel (2012), to obtain a randomized wait-free test-and-set algorithm from Theta(log n) registers, with expected step-complexity Theta(log* n) against the oblivious adversary.

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arXiv2016

Space Bounds for Adaptive Renaming

We study the space complexity of implementing long-lived and one-shot adaptive renaming from multi-reader multi-writer registers, in an asynchronous distributed system with $n$ processes. As a result of an $f$-adaptive renaming algorithm each participating process gets a distinct name in the range $\{1,\dots,f(k)\}$ provided $k$ processes participate. Let $f: \{1,\dots,n\} \rightarrow \mathbb{N}$ be a non-decreasing function satisfying $f(1) \leq n-1$ and let $d = \max\{x ~|~ f(x) \leq n-1\}$. We show that any non-deterministic solo-terminating long-lived $f$-adaptive renaming object requires $d + 1$ registers. This implies a lower bound of $n-c$ registers for long-lived $(k+c)$-adaptive renaming, which we observe is tight. We also prove a lower bound of $\lfloor \frac{2(n - c)}{c+2} \rfloor$ registers for implementing any non-deterministic solo-terminating one-shot $(k+c)$-adaptive renaming. We provide two one-shot renaming algorithms: a wait-free algorithm and an obstruction-free algorithm. Each algorithm employs a parameter to depict the tradeoff between space and adaptivity. When these parameters are chosen appropriately, this results in a wait-free one-shot $(\frac{3k^2}{2})$-adaptive renaming algorithm from $\lceil \sqrt{n} \rceil + 1$ registers, and an obstruction-free one-shot $f$-adaptive renaming algorithm from only $\min\{n, x ~|~ f(x) \geq 2n\} + 1$ registers.

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arXiv2015

On the Time and Space Complexity of ABA Prevention and Detection

We investigate the time and space complexity of detecting and preventing ABAs in shared memory algorithms for systems with n processes and bounded base objects. To that end, we define ABA-detecting registers, which are similar to normal read/write registers, except that they allow a process q to detect with a read operation, whether some process wrote the register since q's last read. ABA-detecting registers can be implemented trivially from a single unbounded register, but we show that they have a high complexity if base objects are bounded: An obstruction-free implementation of an ABA-detecting single bit register cannot be implemented from fewer than n-1 bounded registers. Moreover, bounded CAS objects (or more generally, conditional read-modify-write primitives) offer little help to implement ABA-detecting single bit registers: We prove a linear time-space tradeoff for such implementations. We show that the same time-space tradeoff holds for implementations of single bit LL/SC primitives from bounded writable CAS objects. This proves that the implementations of LL/SC/VL by Anderson and Moir (1995) as well as Jayanti and Petrovic (2003) are optimal. We complement our lower bounds with tight upper bounds: We give an implementation of ABA-detecting registers from n+1 bounded registers, which has step complexity O(1). We also show that (bounded) LL/SC/VL can be implemented from a single bounded CAS object and with O(n) step complexity. Both upper bounds are asymptotically optimal with respect to their time-space product. These results give formal evidence that the ABA problem is inherently difficult, that even writable CAS objects do not provide significant benefits over registers for dealing with the ABA problem itself, and that there is no hope of finding a more efficient implementation of LL/SC/VL from bounded CAS objects and registers than the ones mentioned.

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arXiv2013

Tight Lower Bounds for Greedy Routing in Higher-Dimensional Small-World Grids

We consider Kleinberg's celebrated small world graph model (Kleinberg, 2000), in which a D-dimensional grid {0,...,n-1}^D is augmented with a constant number of additional unidirectional edges leaving each node. These long range edges are determined at random according to a probability distribution (the augmenting distribution), which is the same for each node. Kleinberg suggested using the inverse D-th power distribution, in which node v is the long range contact of node u with a probability proportional to ||u-v||^(-D). He showed that such an augmenting distribution allows to route a message efficiently in the resulting random graph: The greedy algorithm, where in each intermediate node the message travels over a link that brings the message closest to the target w.r.t. the Manhattan distance, finds a path of expected length O(log^2 n) between any two nodes. In this paper we prove that greedy routing does not perform asymptotically better for any uniform and isotropic augmenting distribution, i.e., the probability that node u has a particular long range contact v is independent of the labels of u and v and only a function of ||u-v||. In order to obtain the result, we introduce a novel proof technique: We define a budget game, in which a token travels over a game board, while the player manages a "probability budget". In each round, the player bets part of her remaining probability budget on step sizes. A step size is chosen at random according to a probability distribution of the player's bet. The token then makes progress as determined by the chosen step size, while some of the player's bet is removed from her probability budget. We prove a tight lower bound for such a budget game, and then obtain a lower bound for greedy routing in the D-dimensional grid by a reduction.

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arXiv2012

RMR-Efficient Randomized Abortable Mutual Exclusion

Recent research on mutual exclusion for shared-memory systems has focused on "local spin" algorithms. Performance is measured using the "remote memory references" (RMRs) metric. As common in recent literature, we consider a standard asynchronous shared memory model with N processes, which allows atomic read, write and compare-and-swap (short: CAS) operations. In such a model, the asymptotically tight upper and lower bound on the number of RMRs per passage through the Critical Section is Theta(log N) for the optimal deterministic algorithms (see Yang and Anderson,1995, and Attiya, Hendler and Woelfel, 2008). Recently, several randomized algorithms have been devised that break the Omega(log N) barrier and need only o(log N) RMRs per passage in expectation (see Hendler and Woelfel, 2010, Hendler and Woelfel, 2011, and Bender and Gilbert, 2011). In this paper we present the first randomized "abortable" mutual exclusion algorithm that achieves a sub-logarithmic expected RMR complexity. More precisely, against a weak adversary (which can make scheduling decisions based on the entire past history, but not the latest coin-flips of each process) every process needs an expected number of O(log N/ log log N) RMRs to enter end exit the critical section. If a process receives an abort-signal, it can abort an attempt to enter the critical section within a finite number of its own steps and by incurring O(log N/ log log N) RMRs.

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arXiv2012

Explicit and Efficient Hash Families Suffice for Cuckoo Hashing with a Stash

It is shown that for cuckoo hashing with a stash as proposed by Kirsch, Mitzenmacher, and Wieder (2008) families of very simple hash functions can be used, maintaining the favorable performance guarantees: with stash size $s$ the probability of a rehash is $O(1/n^{s+1})$, and the evaluation time is $O(s)$. Instead of the full randomness needed for the analysis of Kirsch et al. and of Kutzelnigg (2010) (resp. $Θ(\log n)$-wise independence for standard cuckoo hashing) the new approach even works with 2-wise independent hash families as building blocks. Both construction and analysis build upon the work of Dietzfelbinger and Woelfel (2003). The analysis, which can also be applied to the fully random case, utilizes a graph counting argument and is much simpler than previous proofs. As a byproduct, an algorithm for simulating uniform hashing is obtained. While it requires about twice as much space as the most space efficient solutions, it is attractive because of its simple and direct structure.

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arXiv2011

The Space Complexity of Long-lived and One-Shot Timestamp Implementations

This paper is concerned with the problem of implementing an unbounded timestamp object from multi-writer atomic registers, in an asynchronous distributed system of n processors with distinct identifiers where timestamps are taken from an arbitrary universe. Ellen, Fatourou and Ruppert (2008) showed that sqrt{n}/2-O(1) registers are required for any obstruction-free implementation of long-lived timestamp systems from atomic registers (meaning processors can repeatedly get timestamps). We improve this existing lower bound in two ways. First we establish a lower bound of n/6 - O(1) registers for the obstruction-free long-lived timestamp problem. Previous such linear lower bounds were only known for constrained versions of the timestamp problem. This bound is asymptotically tight; Ellen, Fatourou and Ruppert (2008) constructed a wait-free algorithm that uses n-1 registers. Second we show that sqrt{n} - O(1) registers are required for any obstruction-free implementation of one-shot timestamp systems(meaning each processor can get a timestamp at most once). We show that this bound is also asymptotically tight by providing a wait-free one-shot timestamp system that uses fewer than 2 sqrt{n} registers, thus establishing a space complexity gap between one-shot and long-lived timestamp systems.

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arXiv2011

Independence of Tabulation-Based Hash Classes

A tabulation-based hash function maps a key into d derived characters indexing random values in tables that are then combined with bitwise xor operations to give the hash. Thorup and Zhang (2004) presented d-wise independent tabulation-based hash classes that use linear maps over finite fields to map a key, considered as a vector (a,b), to derived characters. We show that a variant where the derived characters are a+b*i for i=0,..., q-1 (using integer arithmetic) yielding (2d-1)-wise independence. Our analysis is based on an algebraic property that characterizes k-wise independence of tabulation-based hashing schemes, and combines this characterization with a geometric argument. We also prove a non-trivial lower bound on the number of derived characters necessary for k-wise independence with our and related hash classes.

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arXiv2011

Linearizable Implementations Do Not Suffice for Randomized Distributed Computation

Linearizability is the gold standard among algorithm designers for deducing the correctness of a distributed algorithm using implemented shared objects from the correctness of the corresponding algorithm using atomic versions of the same objects. We show that linearizability does not suffice for this purpose when processes can exploit randomization, and we discuss the existence of alternative correctness conditions.

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arXiv2008

Tight Bounds for Blind Search on the Integers

We analyze a simple random process in which a token is moved in the interval $A=\{0,...,n\$: Fix a probability distribution $μ$ over $\{1,...,n\$. Initially, the token is placed in a random position in $A$. In round $t$, a random value $d$ is chosen according to $μ$. If the token is in position $a\geq d$, then it is moved to position $a-d$. Otherwise it stays put. Let $T$ be the number of rounds until the token reaches position 0. We show tight bounds for the expectation of $T$ for the optimal distribution $μ$. More precisely, we show that $\min_μ\{E_μ(T)\=Θ((\log n)^2)$. For the proof, a novel potential function argument is introduced. The research is motivated by the problem of approximating the minimum of a continuous function over $[0,1]$ with a ``blind'' optimization strategy.

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