arXiv subjects

Joan Boyar

Publications and source records attributed to Joan Boyar.

At least 19 recordsLinked to original sources

arXiv2026

On the Online Weighted Non-Crossing Matching Problem

We introduce and study the weighted version of an online matching problem in the Euclidean plane with non-crossing constraints: points with non-negative weights arrive online, and an algorithm can match an arriving point to one of the unmatched previously arrived points. In the classic model, the decision on how to match (if at all) a newly arriving point is irrevocable. The goal is to maximize the total weight of matched points under the constraint that straight-line segments corresponding to the edges of the matching do not intersect. The unweighted version of the problem was introduced in the offline setting by Atallah in 1985, and this problem became a subject of study in the online setting with and without advice in several recent papers. We observe that deterministic online algorithms cannot guarantee a non-trivial competitive ratio for the weighted problem, but we give upper and lower bounds on the problem with bounded weights. In contrast to the deterministic case, we show that using randomization, a constant competitive ratio is possible for arbitrary weights. We also study other variants of the problem, including revocability and collinear points, both of which permit non-trivial online algorithms, and we give upper and lower bounds for the attainable competitive ratios. Finally, we prove an advice complexity bound for obtaining optimality, improving the best known bound.

cs.DS↗

arXiv2026

Forwarding Packets Greedily on the Line

We consider the problem of forwarding packets arriving online with their destinations in a line network. In each time step, each router can forward one packet along the edge to its right, and the packet arrives at the next router one time step later. Packets are forwarded until they reach their destination. The flow time of a packet is the elapsed time between its release and its arrival at its destination. The goal is to minimize the maximum flow time. This problem was introduced by Antoniadis et al. in 2014, with a focus on line networks. They proposed several natural algorithms. For one, they proved that it is not $O(1)$-competitive; for others, they claimed analogous lower bounds, seemingly leaving no natural candidate for an $O(1)$-competitive algorithm. In this paper, we study a natural algorithm not considered in that work. Our algorithm, simply called Greedy, selects packets according to their projected flow time under the assumption that they are not delayed any further. We focus on the special case in which each packet needs to be forwarded by one or two routers; this case captures core difficulties. We show that Greedy achieves a competitive ratio of exactly $2-2^{1-k}$, where $k$ is the number of active routers in the network. We also give the first nontrivial general lower bound, which applies even to randomized algorithms: using the same type of instances as in our lower bound for Greedy, we show that no algorithm can be $(4/3-\varepsilon)$-competitive for any $\varepsilon>0$.

cs.DS↗

arXiv2025

Distributed Graph Algorithms with Predictions

We initiate the study of deterministic distributed graph algorithms with predictions in synchronous message passing systems. The process at each node in the graph is given a prediction, which is some extra information about the problem instance that may be incorrect. The processes may use the predictions to help them solve the problem. The overall goal is to develop algorithms that both work faster when predictions are good and do not work much worse than algorithms without predictions when predictions are bad. Concepts from the more general area of algorithms with predictions, such as error measures, consistency, robustness, and smoothness, are adapted to distributed graph algorithms with predictions. We consider algorithms with predictions for distributed graph problems, where each node is given a prediction for its output. We present a framework for evaluating distributed graph algorithms with predictions and methods for transforming existing algorithms without predictions to effectively use predictions. Our approach is illustrated by developing algorithms with predictions for the Maximal Independent Set problem. We also include a discussion of error measures and demonstrate how fine-tuning an error measure towards a particular problem can yield stronger results about the performance of algorithms for that problem.

cs.DC↗

arXiv2025

Online Interval Scheduling with Predictions

In online interval scheduling, the input is an online sequence of intervals, and the goal is to accept a maximum number of non-overlapping intervals. In the more general disjoint path allocation problem, the input is a sequence of requests, each consisting of pairs of vertices of a known graph, and the goal is to accept a maximum number of requests forming edge-disjoint paths between accepted pairs. We study a setting with a potentially erroneous prediction specifying the set of requests forming the input sequence and provide tight upper and lower bounds on the competitive ratios of online algorithms as a function of the prediction error. We also present asymptotically tight trade-offs between consistency (competitive ratio with error-free predictions) and robustness (competitive ratio with adversarial predictions) of interval scheduling algorithms. Finally, we provide experimental results on real-world scheduling workloads that confirm our theoretical analysis.

cs.DS↗

arXiv2024

Complexity Classes for Online Problems with and without Predictions

With the developments in machine learning, there has been a surge in interest and results focused on algorithms utilizing predictions, not least in online algorithms where most new results incorporate the prediction aspect for concrete online problems. While the structural computational hardness of problems with regards to time and space is quite well developed, not much is known about online problems where time and space resources are typically not in focus. Some information-theoretical insights were gained when researchers considered online algorithms with oracle advice, but predictions of uncertain quality is a very different matter. We initiate the development of a complexity theory for online problems with predictions, considering minimization problems and one prediction bit per request. Based on the most generic hard online problem type, string guessing, we define a family of hierarchies of complexity classes (indexed by pairs of error measures) and develop notions of reductions, class membership, hardness, and completeness. Our framework contains all the tools one expects to find when working with complexity, and we illustrate our tools by analyzing problems with different characteristics. In addition, we show that known lower bounds for paging with discard predictions apply directly to all hard problems for each class in the hierarchy based on the canonical pair of error measures. This paging problem is not complete for these classes. Our work also implies corresponding complexity classes for classic online problems without predictions, with the corresponding complete problems.

cs.DS↗

arXiv2023

Quotable Signatures for Authenticating Shared Quotes

Quotable signature schemes are digital signature schemes with the additional property that from the signature for a message, any party can extract signatures for (allowable) quotes from the message, without knowing the secret key or interacting with the signer of the original message. Crucially, the extracted signatures are still signed with the original secret key. We define a notion of security for quotable signature schemes and construct a concrete example of a quotable signature scheme, using Merkle trees and classical digital signature schemes. The scheme is shown to be secure, with respect to the aforementioned notion of security. Additionally, we prove bounds on the complexity of the constructed scheme and provide algorithms for signing, quoting, and verifying. Finally, concrete use cases of quotable signatures are considered, using them to combat misinformation by bolstering authentic content on social media. We consider both how quotable signatures can be used, and why using them could help mitigate the effects of fake news.

cs.CR↗

arXiv2023

Online Minimum Spanning Trees with Weight Predictions

We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an irrevocable decision must be made regarding whether or not the edge should be included into the spanning tree. In order to assess the quality of our algorithms, we define an appropriate error measure and analyze the performance of the algorithms as a function of the error. We prove that, according to competitive analysis, the simplest algorithm, Follow-the-Predictions, is optimal. However, intuitively, one should be able to do better, and we present a greedy variant of Follow-the-Predictions. In analyzing that algorithm, we believe we present the first random order analysis of a non-trivial online algorithm with predictions, by which we obtain an algorithmic separation. This may be useful for distinguishing between algorithms for other problems when Follow-the-Predictions is optimal according to competitive analysis.

cs.DS↗

arXiv2022

Paging with Succinct Predictions

Paging is a prototypical problem in the area of online algorithms. It has also played a central role in the development of learning-augmented algorithms -- a recent line of research that aims to ameliorate the shortcomings of classical worst-case analysis by giving algorithms access to predictions. Such predictions can typically be generated using a machine learning approach, but they are inherently imperfect. Previous work on learning-augmented paging has investigated predictions on (i) when the current page will be requested again (reoccurrence predictions), (ii) the current state of the cache in an optimal algorithm (state predictions), (iii) all requests until the current page gets requested again, and (iv) the relative order in which pages are requested. We study learning-augmented paging from the new perspective of requiring the least possible amount of predicted information. More specifically, the predictions obtained alongside each page request are limited to one bit only. We consider two natural such setups: (i) discard predictions, in which the predicted bit denotes whether or not it is ``safe'' to evict this page, and (ii) phase predictions, where the bit denotes whether the current page will be requested in the next phase (for an appropriate partitioning of the input into phases). We develop algorithms for each of the two setups that satisfy all three desirable properties of learning-augmented algorithms -- that is, they are consistent, robust and smooth -- despite being limited to a one-bit prediction per request. We also present lower bounds establishing that our algorithms are essentially best possible.

cs.LG↗

arXiv2022

Online Unit Profit Knapsack with Untrusted Predictions

A variant of the online knapsack problem is considered in the settings of trusted and untrusted predictions. In Unit Profit Knapsack, the items have unit profit, and it is easy to find an optimal solution offline: Pack as many of the smallest items as possible into the knapsack. For Online Unit Profit Knapsack, the competitive ratio is unbounded. In contrast, previous work on online algorithms with untrusted predictions generally studied problems where an online algorithm with a constant competitive ratio is known. The prediction, possibly obtained from a machine learning source, that our algorithm uses is the average size of those smallest items that fit in the knapsack. For the prediction error in this hard online problem, we use the ratio $r=\frac{a}{\hat{a}}$ where $a$ is the actual value for this average size and $\hat{a}$ is the prediction. The algorithm presented achieves a competitive ratio of $\frac{1}{2r}$ for $r\geq 1$ and $\frac{r}{2}$ for $r\leq 1$. Using an adversary technique, we show that this is optimal in some sense, giving a trade-off in the competitive ratio attainable for different values of $r$. Note that the result for accurate advice, $r=1$, is only $\frac{1}{2}$, but we show that no algorithm knowing the value $a$ can achieve a competitive ratio better than $\frac{e-1}{e}\approx 0.6321$ and present an algorithm with a matching upper bound. We also show that this latter algorithm attains a competitive ratio of $r\frac{e-1}{e}$ for $r \leq 1$ and $\frac{e-r}{e}$ for $1 \leq r < e$, and no algorithm can be better for both $r<1$ and $1\leq r<e$.

cs.DS↗

arXiv2022

Advice Complexity of Adaptive Priority Algorithms

The priority model was introduced to capture "greedy-like" algorithms. Motivated by the success of advice complexity in the area of online algorithms, the fixed priority model was extended to include advice, and a reduction-based framework was developed for proving lower bounds on the amount of advice required to achieve certain approximation ratios in this rather powerful model. To capture most of the algorithms that are considered greedy-like, the even stronger model of adaptive priority algorithms is needed. We extend the adaptive priority model to include advice. We modify the reduction-based framework from the fixed priority case to work with the more powerful adaptive priority algorithms, simplifying the proof of correctness and strengthening all previous lower bounds by a factor of two in the process. We also present a purely combinatorial adaptive priority algorithm with advice for Minimum Vertex Cover on triangle-free graphs of maximum degree three. Our algorithm achieves optimality and uses at most 7n/22 bits of advice. No adaptive priority algorithm without advice can achieve optimality without advice, and we prove that an online algorithm with advice needs more than 7n/22 bits of advice to reach optimality. We show connections between exact algorithms and priority algorithms with advice. The branching in branch-and-reduce algorithms can be seen as trying all possible advice strings, and all priority algorithms with advice that achieve optimality define corresponding exact algorithms, priority exact algorithms. Lower bounds on advice-based adaptive algorithms imply lower bounds on running times of exact algorithms designed in this way.

cs.DS↗

arXiv2020

Online Bin Covering with Advice

The bin covering problem asks for covering a maximum number of bins with an online sequence of $n$ items of different sizes in the range $(0,1]$; a bin is said to be covered if it receives items of total size at least 1. We study this problem in the advice setting and provide tight bounds for the size of advice required to achieve optimal solutions. Moreover, we show that any algorithm with advice of size $o(\log \log n)$ has a competitive ratio of at most 0.5. In other words, advice of size $o(\log \log n)$ is useless for improving the competitive ratio of 0.5, attainable by an online algorithm without advice. This result highlights a difference between the bin covering and the bin packing problems in the advice model: for the bin packing problem, there are several algorithms with advice of constant size that outperform online algorithms without advice. Furthermore, we show that advice of size $O(\log \log n)$ is sufficient to achieve a competitive ratio that is arbitrarily close to $0.53\bar{3}$ and hence strictly better than the best ratio $0.5$ attainable by purely online algorithms. The technicalities involved in introducing and analyzing this algorithm are quite different from the existing results for the bin packing problem and confirm the different nature of these two problems. Finally, we show that a linear number of bits of advice is necessary to achieve any competitive ratio better than 15/16 for the online bin covering problem.

cs.DS↗

arXiv2018

Online Dominating Set

This paper is devoted to the online dominating set problem and its variants. We believe the paper represents the first systematic study of the effect of two limitations of online algorithms: making irrevocable decisions while not knowing the future, and being incremental, i.e., having to maintain solutions to all prefixes of the input. This is quantified through competitive analyses of online algorithms against two optimal algorithms, both knowing the entire input, but only one having to be incremental. We also consider the competitive ratio of the weaker of the two optimal algorithms against the other. We consider important graph classes, distinguishing between connected and not necessarily connected graphs. For the classic graph classes of trees, bipartite, planar, and general graphs, we obtain tight results in almost all cases. We also derive upper and lower bounds for the class of bounded-degree graphs. From these analyses, we get detailed information regarding the significance of the necessary requirement that online algorithms be incremental. In some cases, having to be incremental fully accounts for the online algorithm's disadvantage.

cs.DS↗

arXiv2018

Advice Complexity of Priority Algorithms

The priority model of "greedy-like" algorithms was introduced by Borodin, Nielsen, and Rackoff in 2002. We augment this model by allowing priority algorithms to have access to advice, i.e., side information precomputed by an all-powerful oracle. Obtaining lower bounds in the priority model without advice can be challenging and may involve intricate adversary arguments. Since the priority model with advice is even more powerful, obtaining lower bounds presents additional difficulties. We sidestep these difficulties by developing a general framework of reductions which makes lower bound proofs relatively straightforward and routine. We start by introducing the Pair Matching problem, for which we are able to prove strong lower bounds in the priority model with advice. We develop a template for constructing a reduction from Pair Matching to other problems in the priority model with advice -- this part is technically challenging since the reduction needs to define a valid priority function for Pair Matching while respecting the priority function for the other problem. Finally, we apply the template to obtain lower bounds for a number of standard discrete optimization problems.

cs.DS↗

arXiv2018

The Scheduler is Very Powerful in Competitive Analysis of Distributed List Accessing

This work is a continuation of efforts to define and understand competitive analysis of algorithms in a distributed shared memory setting, which is surprisingly different from the classical online setting. In fact, in a distributed shared memory setting, we find a counter-example to the theorem concerning classical randomized online algorithms which shows that, if there is a $c$-competitive randomized algorithm against an adaptive offline adversary, then there is a $c$-competitive deterministic algorithm [Ben-David, Borodin, Karp, Tardos, Wigderson, 1994]. In a distributed setting, there is additional lack of knowledge concerning what the other processes have done. There is also additional power for the adversary, having control of the scheduler which decides when each process is allowed to take steps. We consider the list accessing problem, which is a benchmark problem for sequential online algorithms. In the distributed version of this problem, each process has its own finite sequence of requests to a shared list. The scheduler arises as a major issue in its competitive analysis. We introduce two different adversaries, which differ in how they are allowed to schedule processes, and use them to perform competitive analysis of distributed list accessing. We prove tight upper and lower bounds on combinatorial properties of merges of the request sequences, which we use in the analysis. Our analysis shows that the effects of the adversarial scheduler can be quite significant, dominating the usual quality loss due to lack of information about the future.

cs.DS↗

arXiv2018

Tight Bounds for Restricted Grid Scheduling

The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to minimize the total size of all the bins used. Previously, a lower bound of 5/4 on the competitive ratio of this problem was achieved using jobs of size S and 2S-1. For these item sizes and maximum bin size 4S-3, we obtain asymptotically matching upper and lower bounds, which vary depending on the ratio of the number of small jobs to the number of large jobs.

cs.DS↗

arXiv2018

Multiplicative Complexity of Vector Valued Boolean Functions

We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $ΣΠΣ$ circuits, we show that there is a tight connection between error correcting codes and circuits computing functions with high nonlinearity. Combining this with known coding theory results, we show that functions with $n$ inputs and $n$ outputs with the highest possible nonlinearity must have at least $2.32n$ AND gates. We further show that one cannot prove stronger lower bounds by only appealing to the nonlinearity of a function; we show a bilinear circuit computing a function with almost optimal nonlinearity with the number of AND gates being exactly the length of such a shortest code. Additionally we provide a function which, for general circuits, has multiplicative complexity at least $2n-3$. Finally we study the multiplicative complexity of "almost all" functions. We show that every function with $n$ bits of input and $m$ bits of output can be computed using at most $2.5(1+o(1))\sqrt{m2^n}$ AND gates.

cs.CC↗

arXiv2018

Relative Worst-Order Analysis: A Survey

Relative worst-order analysis is a technique for assessing the relative quality of online algorithms. We survey the most important results obtained with this technique and compare it with other quality measures.

cs.DS↗

arXiv2017

Weighted Online Problems with Advice

Recently, the first online complexity class, AOC, was introduced. The class consists of many online problems where each request must be either accepted or rejected, and the aim is to either minimize or maximize the number of accepted requests, while maintaining a feasible solution. All AOC-complete problems (including Independent Set, Vertex Cover, Dominating Set, and Set Cover) have essentially the same advice complexity. In this paper, we study weighted versions of problems in AOC, i.e., each request comes with a weight and the aim is to either minimize or maximize the total weight of the accepted requests. In contrast to the unweighted versions, we show that there is a significant difference in the advice complexity of complete minimization and maximization problems. We also show that our algorithmic techniques for dealing with weighted requests can be extended to work for non-complete AOC problems such as maximum matching (giving better results than what follow from the general AOC results) and even non-AOC problems such as scheduling.

cs.DS↗