Algorithmica最新文献

{"title":"Anti-factor is FPT Parameterized by Treewidth and List Size (but Counting is Hard)","authors":"Dániel Marx,&nbsp;Govind S. Sankar,&nbsp;Philipp Schepper","doi":"10.1007/s00453-024-01265-w","DOIUrl":"10.1007/s00453-024-01265-w","url":null,"abstract":"<div><p>In the general <span>AntiFactor</span> problem, a graph <i>G</i> and, for every vertex <i>v</i> of <i>G</i>, a set <span>(X_vsubseteq {mathbb {N}})</span> of forbidden degrees is given. The task is to find a set <i>S</i> of edges such that the degree of <i>v</i> in <i>S</i> is <i>not</i> in the set <span>(X_v)</span>. Standard techniques (dynamic programming plus fast convolution) can be used to show that if <i>M</i> is the largest forbidden degree, then the problem can be solved in time <span>((M+2)^{{operatorname {tw}}}cdot n^{{mathcal {O}}(1)})</span> if a tree decomposition of width <span>({operatorname {tw}})</span> is given. However, significantly faster algorithms are possible if the sets <span>(X_v)</span> are sparse: our main algorithmic result shows that if every vertex has at most <span>(x)</span> forbidden degrees (we call this special case <span>AntiFactor</span>_x), then the problem can be solved in time <span>((x+1)^{{mathcal {O}}({operatorname {tw}})}cdot n^{{mathcal {O}}(1)})</span>. That is, <span>AntiFactor</span>_x is fixed-parameter tractable parameterized by treewidth <span>({operatorname {tw}})</span> and the maximum number <span>(x)</span> of excluded degrees. Our algorithm uses the technique of representative sets, which can be generalized to the optimization version, but (as expected) not to the counting version of the problem. In fact, we show that #<span>AntiFactor</span>₁ is already #<span>W</span> <span>([1])</span>-hard parameterized by the width of the given decomposition. Moreover, we show that, unlike for the decision version, the standard dynamic programming algorithm is essentially optimal for the counting version. Formally, for a fixed nonempty set <span>(X)</span>, we denote by <span>(X)</span>-<span>AntiFactor</span> the special case where every vertex <i>v</i> has the same set <span>(X_v=X)</span> of forbidden degrees. We show the following lower bound for every fixed set <span>(X)</span>: if there is an <span>(epsilon &gt;0)</span> such that #<span>(X)</span>-<span>AntiFactor</span> can be solved in time <span>((max X+2-epsilon )^{{operatorname {tw}}}cdot n^{{mathcal {O}}(1)})</span> given a tree decomposition of width <span>({operatorname {tw}})</span>, then the counting strong exponential-time hypothesis (#SETH) fails.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 1","pages":"22 - 88"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01265-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy Constrained Depth First Search","authors":"Shantanu Das,&nbsp;Dariusz Dereniowski,&nbsp;Przemysław Uznański","doi":"10.1007/s00453-024-01275-8","DOIUrl":"10.1007/s00453-024-01275-8","url":null,"abstract":"<div><p>Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such a route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this is asymptotically optimal over all exploration strategies. This paper considers a variant of such search strategies where the length of each route is bounded by a positive integer <i>B</i> (e.g. due to limited energy resources of the searcher). The objective is to cover all the edges of a tree <i>T</i> using the minimum number of routes, each starting and ending at the root and each being of length at most <i>B</i>. To this end, we analyze the following natural greedy tree traversal process that is based on decomposing a depth first search traversal into a sequence of limited length routes. Given any arbitrary depth first search traversal <i>R</i> of the tree <i>T</i>, we cover <i>R</i> with routes <span>(R_1,ldots ,R_l)</span>, each of length at most <i>B</i> such that: <span>(R_i)</span> starts at the root, reaches directly the farthest point of <i>R</i> visited by <span>(R_{i-1})</span>, then <span>(R_i)</span> continues along the path <i>R</i> as far as possible, and finally <span>(R_i)</span> returns to the root. We call the above algorithm <i>piecemeal-DFS</i> and we prove that it achieves the asymptotically minimal number of routes <i>l</i>, regardless of the choice of <i>R</i>. Our analysis also shows that the total length of the traversal (and thus the traversal time) of piecemeal-DFS is asymptotically minimum over all energy-constrained exploration strategies. The fact that <i>R</i> can be chosen arbitrarily means that the exploration strategy can be constructed in an online fashion when the input tree <i>T</i> is not known in advance. Each route <span>(R_i)</span> can be constructed without any knowledge of the yet unvisited part of <i>T</i>. Surprisingly, our results show that depth first search is efficient for energy constrained exploration of trees, even though it is known that the same does not hold for energy constrained exploration of arbitrary graphs.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 12","pages":"3759 - 3782"},"PeriodicalIF":0.9,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01275-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Scheduling Mechanisms Beyond the Worst Case","authors":"Yansong Gao,&nbsp;Jie Zhang","doi":"10.1007/s00453-024-01277-6","DOIUrl":"10.1007/s00453-024-01277-6","url":null,"abstract":"<div><p>The problem of scheduling unrelated machines has been studied since the inception of algorithmic mechanism design (Nisan and Ronen, Algorithmic mechanism design(extended abstract). In: Proceedings of the Thirty First Annual ACM Symposium on Theory of Computing (STOC), pp. 129–140, 1999. It is a resource allocation problem that entails assigning <i>m</i> tasks to <i>n</i> machines for execution. Machines are regarded as strategic agents who may lie about their execution costs so as to minimize their time cost. To address the situation when monetary payment is not an option to compensate the machines’ costs, Koutsoupias (Theory Comput Syst 54:375–387, 2014) devised two <i>truthful</i> mechanisms, K and P respectively, that achieves an approximation ratio of <span>(frac{n+1}{2})</span> and <i>n</i>, for social cost minimization. In addition, no truthful mechanism can achieve an approximation ratio better than <span>(frac{n+1}{2})</span>. Hence, mechanism K is optimal. While the approximation ratio provides a strong worst-case guarantee, it also limits us to a comprehensive understanding of mechanism performance on various inputs. This paper investigates these two scheduling mechanisms beyond the worst case. We first show that mechanism K achieves a smaller social cost than mechanism P on every input. That is, mechanism K is pointwise better than mechanism P. Next, for each task, when machines’ execution costs are independent and identically drawn from a task-specific distribution, we show that the average-case approximation ratio of mechanism K converges to a constant determined by the task-specific distribution. This bound is tight for mechanism K. For a better understanding of this distribution-dependent constant, on the one hand, we estimate its value by plugging in a few common distributions; on the other, we show that this converging bound improves a known bound (Zhang in Algorithmica 83(6):1638–1652, 2021)) which only captures the single-task setting. Last, we find that the average-case approximation ratio of mechanism P converges to the same constant.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 1","pages":"1 - 21"},"PeriodicalIF":0.9,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01277-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Recovering the Original Simplicity: Succinct and Exact Quantum Algorithm for the Welded Tree Problem","authors":"Guanzhong Li,&nbsp;Lvzhou Li,&nbsp;Jingquan Luo","doi":"10.1007/s00453-024-01273-w","DOIUrl":"10.1007/s00453-024-01273-w","url":null,"abstract":"<div><p>This work revisits quantum algorithms for the well-known welded tree problem, proposing a succinct quantum algorithm based on the simple coined quantum walks. It iterates the naturally defined coined quantum walk operator for a classically precomputed number of iterations, and measures. The number of iterations is linear in the depth of the tree. The success probability of this procedure is inversely linear in the depth of the tree. Moreover, it is the same for all instances of the problem of a fixed size, therefore, we can use the exact quantum amplitude amplification subroutine to answer with probability 1. This gives an exponential speedup over any classical algorithm for the same problem. The significance of the results may be seen as follows. (i) Our algorithm is rather simple compared with the one in (Jeffery and Zur, STOC’2023), which not only breaks the stereotype that coined quantum walks can only achieve quadratic speedups over classical algorithms, but also demonstrates the power of the simplest quantum walk model. (ii) Our algorithm achieves certainty of success for the first time. Thus, it becomes one of the few examples that exhibit exponential separation between exact quantum and randomized query complexities.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 12","pages":"3719 - 3758"},"PeriodicalIF":0.9,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Permutation-constrained Common String Partitions with Applications","authors":"Manuel Lafond,&nbsp;Binhai Zhu","doi":"10.1007/s00453-024-01276-7","DOIUrl":"10.1007/s00453-024-01276-7","url":null,"abstract":"<div><p>We study a new combinatorial problem based on the famous Minimum Common String Partition problem, which we call Permutation-constrained Common String Partition (PCSP for short). In PCSP, we are given two sequences/genomes <i>s</i> and <i>t</i> with the same length and a permutation <span>(pi )</span> on <span>([ell ])</span>, the question is to decide whether it is possible to decompose <i>s</i> and <i>t</i> into <span>(ell )</span> blocks that can be matched according to some specified requirements, and that conform with the permutation <span>(pi )</span>. Our main result is that PCSP is FPT in parameter <span>(ell + d)</span>, where <i>d</i> is the maximum number of occurrences that any symbol may have in <i>s</i> or <i>t</i>. We also study a variant where the input specifies whether each matched pair of block needs to be preserved as is, or reversed. With this result on PCSP, we show that a series of genome rearrangement problems are FPT <span>(k + d)</span>, where <i>k</i> is the rearrangement distance between two genomes of interest.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 12","pages":"3684 - 3718"},"PeriodicalIF":0.9,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reachability of Fair Allocations via Sequential Exchanges","authors":"Ayumi Igarashi,&nbsp;Naoyuki Kamiyama,&nbsp;Warut Suksompong,&nbsp;Sheung Man Yuen","doi":"10.1007/s00453-024-01271-y","DOIUrl":"10.1007/s00453-024-01271-y","url":null,"abstract":"<div><p>In the allocation of indivisible goods, a prominent fairness notion is envy-freeness up to one good (EF1). We initiate the study of reachability problems in fair division by investigating the problem of whether one EF1 allocation can be reached from another EF1 allocation via a sequence of exchanges such that every intermediate allocation is also EF1. We show that two EF1 allocations may not be reachable from each other even in the case of two agents, and deciding their reachability is PSPACE-complete in general. On the other hand, we prove that reachability is guaranteed for two agents with identical or binary utilities as well as for any number of agents with identical binary utilities. We also examine the complexity of deciding whether there is an EF1 exchange sequence that is optimal in the number of exchanges required.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 12","pages":"3653 - 3683"},"PeriodicalIF":0.9,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01271-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Flipping the Fréchet Distance","authors":"Omrit Filtser,&nbsp;Mayank Goswami,&nbsp;Joseph S. B. Mitchell,&nbsp;Valentin Polishchuk","doi":"10.1007/s00453-024-01267-8","DOIUrl":"10.1007/s00453-024-01267-8","url":null,"abstract":"<div><p>The classical and extensively-studied <i>Fréchet distance</i> between two curves is defined as an <i>inf max</i>, where the infimum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this article we investigate a “flipped” Fréchet measure defined by a <i>sup min</i> – the supremum is over all traversals of the curves, and the minimum is over all concurrent positions of the two agents. This measure produces a notion of “social distance” between two curves (or general domains), where agents traverse curves while trying to stay as far apart as possible. We first study the flipped Fréchet measure between two polygonal curves in one and two dimensions, providing conditional lower bounds and matching algorithms. We then consider this measure on polygons, where it denotes the minimum distance that two agents can maintain while restricted to travel in or on the boundary of the same polygon. We investigate several variants of the problem in this setting, for some of which we provide linear-time algorithms. We draw connections between our proposed flipped Fréchet measure and existing related work in computational geometry, hoping that our new measure may spawn investigations akin to those performed for the Fréchet distance, and into further interesting problems that arise.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 12","pages":"3629 - 3652"},"PeriodicalIF":0.9,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semi-streaming Algorithms for Submodular Function Maximization Under b-Matching, Matroid, and Matchoid Constraints","authors":"Chien-Chung Huang,&nbsp;François Sellier","doi":"10.1007/s00453-024-01272-x","DOIUrl":"10.1007/s00453-024-01272-x","url":null,"abstract":"<div><p>We consider the problem of maximizing a non-negative submodular function under the <i>b</i>-matching constraint, in the semi-streaming model. When the function is linear, monotone, and non-monotone, we obtain the approximation ratios of <span>(2+varepsilon )</span>, <span>(3 + 2 sqrt{2} approx 5.828)</span>, and <span>(4 + 2 sqrt{3} approx 7.464)</span>, respectively. We also consider a generalized problem, where a <i>k</i>-uniform hypergraph is given, along with an extra matroid or a <span>(k')</span>-matchoid constraint imposed on the edges, with the same goal of finding a <i>b</i>-matching that maximizes a submodular function. When the extra constraint is a matroid, we obtain the approximation ratios of <span>(k + 1 + varepsilon )</span>, <span>(k + 2sqrt{k+1} + 2)</span>, and <span>(k + 2sqrt{k + 2} + 3)</span> for linear, monotone and non-monotone submodular functions, respectively. When the extra constraint is a <span>(k')</span>-matchoid, we attain the approximation ratio <span>(frac{8}{3}k+ frac{64}{9}k' + O(1))</span> for general submodular functions.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 11","pages":"3598 - 3628"},"PeriodicalIF":0.9,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Parameterized Complexity of Compact Set Packing","authors":"Ameet Gadekar","doi":"10.1007/s00453-024-01269-6","DOIUrl":"10.1007/s00453-024-01269-6","url":null,"abstract":"<div><p>The <span>Set Packing</span> problem is, given a collection of sets <span>(mathcal {S})</span> over a ground set <i>U</i>, to find a maximum collection of sets that are pairwise disjoint. The problem is among the most fundamental NP-hard optimization problems that have been studied extensively in various computational regimes. The focus of this work is on parameterized complexity, <span>Parameterized Set Packing</span> (<span>PSP</span>): Given parameter <span>(r in {mathbb N})</span>, is there a collection <span>( mathcal {S}' subseteq mathcal {S}: |mathcal {S}'| = r)</span> such that the sets in <span>(mathcal {S}')</span> are pairwise disjoint? Unfortunately, the problem is not fixed parameter tractable unless <span>(textsf {W[1]} = textsf {FPT} )</span>, and, in fact, an “enumerative” running time of <span>(|mathcal {S}|^{Omega (r)})</span> is required unless the exponential time hypothesis (ETH) fails. This paper is a quest for tractable instances of <span>Set Packing</span> from parameterized complexity perspectives. We say that the input <span>(({U},mathcal {S}))</span> is “compact” if <span>(|{U}| = f(r)cdot textsf {poly} ( log |mathcal {S}|))</span>, for some <span>(f(r) ge r)</span>. In the <span>Compact PSP</span> problem, we are given a compact instance of <span>PSP</span>. In this direction, we present a “dichotomy” result of <span>PSP</span>: When <span>(|{U}| = f(r)cdot o(log |mathcal {S}|))</span>, <span>PSP</span> is in <span>FPT</span>, while for <span>(|{U}| = rcdot Theta (log (|mathcal {S}|)))</span>, the problem is <span>W[1]</span>-hard; moreover, assuming ETH, <span>Compact PSP</span> does not admit <span>(|mathcal {S}|^{o(r/log r)})</span> time algorithm even when <span>(|{U}| = rcdot Theta (log (|mathcal {S}|)))</span>. Although certain results in the literature imply hardness of compact versions of related problems such as <span>Set</span> <span>(r)</span><span>-Covering</span> and <span>Exact</span> <span>(r)</span><span>-Covering</span>, these constructions fail to extend to <span>Compact PSP</span>. A novel contribution of our work is the identification and construction of a gadget, which we call Compatible Intersecting Set System pair, that is crucial in obtaining the hardness result for <span>Compact PSP</span>. Finally, our framework can be extended to obtain improved running time lower bounds for <span>Compact</span> <span>(r)</span><span>-VectorSum</span>.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 11","pages":"3579 - 3597"},"PeriodicalIF":0.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01269-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ultimate Greedy Approximation of Independent Sets in Subcubic Graphs","authors":"Piotr Krysta,&nbsp;Mathieu Mari,&nbsp;Nan Zhi","doi":"10.1007/s00453-024-01268-7","DOIUrl":"10.1007/s00453-024-01268-7","url":null,"abstract":"<div><p>We study the approximability of the maximum size independent set (MIS) problem in bounded degree graphs. This is one of the most classic and widely studied NP-hard optimization problems. It is known for its inherent hardness of approximation. We focus on the well known minimum-degree greedy algorithm for this problem. This algorithm iteratively chooses a minimum degree vertex in the graph, adds it to the solution and removes its neighbors, until the remaining graph is empty. The approximation ratios of this algorithm have been widely studied, where it is augmented with an advice that tells the greedy algorithm which minimum degree vertex to choose if it is not unique. Our main contribution is a new mathematical theory for the design of such greedy algorithms for MIS with efficiently computable advice and for the analysis of their approximation ratios. Using this theory we obtain the ultimate approximation ratio of 5/4 for greedy algorithms on graphs with maximum degree 3, which completely solves an open problem from the paper by Halldórsson and Yoshihara (in: Staples, Eades, Katoh, Moffat (eds) Algorithms and computations—ISAAC ’95, in 2026 LNCS, Springer, Berlin, Heidelberg, 1995) . Our algorithm is the fastest currently known algorithm for MIS with this approximation ratio on such graphs. We also obtain a simple and short proof of the <span>((Delta +2)/3)</span>-approximation ratio of any greedy algorithms on graphs with maximum degree <span>(Delta )</span>, the result proved previously by Halldórsson and Radhakrishnan (Nord J Comput 1:475–492, 1994) . We almost match this ratio by showing a lower bound of <span>((Delta +1)/3)</span> on the ratio of a greedy algorithm that can use an advice. We apply our new algorithm to the minimum vertex cover problem on graphs with maximum degree 3 to obtain a substantially faster 6/5-approximation algorithm than the one currently known. We complement our algorithmic, upper bound results with lower bound results, which show that the problem of designing good advice for greedy algorithms for MIS is computationally hard and even hard to approximate on various classes of graphs. These results significantly improve on the previously known hardness results. Moreover, these results suggest that obtaining the upper bound results on the design and analysis of the greedy advice is non-trivial.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 11","pages":"3518 - 3578"},"PeriodicalIF":0.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}