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Kanstantsin Pashkovich

Publications and source records attributed to Kanstantsin Pashkovich.

At least 19 recordsLinked to original sources
arXiv2026

Efficient Algorithms for Online Subadditive Combinatorial Allocations

For the online combinatorial allocation problem with subadditive valuations, Correa and Cristi (STOC 2023) proved the existence of a $6$-competitive online algorithm, improving on the previous best $O(\log\!\log m)$-competitive online algorithm due to Dütting, Kesselheim, and Lucier (FOCS 2020), where $m$ is the number of items. However, Correa and Cristi's result is existential, and it was left open whether a constant competitive ratio is attainable via an efficient online algorithm that uses a polynomial number of demand oracle queries. In this work, we answer this affirmatively, giving an expected-polynomial-time $(6 + ε)$-competitive online algorithm for any constant $ε> 0$. Our techniques also recover, in the offline setting, the $(2 + ε)$-approximation result of Feige (STOC, 2006). Finally, when the buyers' valuations are drawn from identical distributions, we exploit symmetry to obtain an improved $(60/11+ε)$-competitive algorithm. Starting with the natural configuration LP relaxation for the problem, our main technical contribution is a recursive Bundle Score Generator (BSG) that resolves item conflicts by assigning correlated scores to the items requested by each buyer. Unlike the Random Score Generator whose existence is shown by Correa and Cristi, our BSG is efficiently computable in expected polynomial time. Moreover, it satisfies a stochastic dominance property that is sufficient to recover both Feige's offline result and Correa and Cristi's online result.

cs.DS↗
arXiv2026

Multidimensional Budget-Feasible Mechanism Design

In budget-feasible mechanism design, a buyer wishes to procure a set of items of maximum value from self-interested players. We have a valuation function $v:2^U \to \mathbb{R}_+$, where $U$ is the set of all items, where $v(S)$ specifies the value obtained from set $S$ of items. The entirety of current work on budget-feasible mechanisms has focused on the single-dimensional setting, wherein each player holds a single item $e$ and incurs a private cost $c_e$ for supplying item $e$. We introduce multidimensional budget feasible mechanism design: the universe $U$ is now partitioned into item-sets $\{G_i\}$ held by the different players, and each player $i$ incurs a private cost $c_i(S_i)$ for supplying the set $S_i\subseteq G_i$ of items. A budget-feasible mechanism is a mechanism that is truthful, and where the total payment made to the players is at most some given budget $B$. The goal is to devise a budget-feasible mechanism that procures a set of items of large value. We obtain the first approximation guarantees for multidimensional budget feasible mechanism design. Our contributions are threefold. First, we prove an impossibility result showing that the standard benchmark used in single-dimensional budget-feasible mechanism design, namely the algorithmic optimum is inadequate in that no budget-feasible mechanism can achieve good approximation relative to this. We identify that the chief underlying issue here is that there could be a monopolist which prevents a budget-feasible mechanism from obtaining good guarantees. Second, we devise an alternate benchmark, $OPT_{Bench}$, that allows for meaningful approximation guarantees, thereby yielding a metric for comparing mechanisms. Third, we devise budget-feasible mechanisms that achieve constant-factor approximation guarantees with respect to this benchmark for XOS valuations.

cs.GT↗
arXiv2026

A simple Path-based LP Relaxation for Directed Steiner Tree

We study the Directed Steiner Tree (DST) problem in layered graphs through a simple path-based linear programming relaxation. This relaxation achieves an integrality gap of O(l log k), where k is the number of terminals and l is the number of layers, which matches the best known bounds for DST previously obtained via lift-and-project hierarchies. Our formulation bypasses hierarchy machinery, offering a more transparent route to the state-of-the-art bound, and it can be exploited to provide an alternative simpler proof that O(l) rounds of the Sherali-Adams hierarchy suffice for reducing the integrality gap on layered instances of DST.

cs.DS↗
arXiv2026

An $O(\log \log n)$-approximate budget feasible mechanism for subadditive valuations

In budget-feasible mechanism design, there is a set of items $U$, each owned by a distinct seller. The seller of item $e$ incurs a private cost $\overline{c}_e$ for supplying her item. A buyer wishes to procure a set of items from the sellers of maximum value, where the value of a set $S\subseteq U$ of items is given by a valuation function $v:2^U\to \mathbb{R}_+$. The buyer has a budget of $B \in \mathbb{R}_+$ for the total payments made to the sellers. We wish to design a mechanism that is truthful, that is, sellers are incentivized to report their true costs, budget-feasible, that is, the sum of the payments made to the sellers is at most the budget $B$, and that outputs a set whose value is large compared to $\text{OPT}:=\max\{v(S):\overline{c}(S)\le B,S\subseteq U\}$. Budget-feasible mechanism design has been extensively studied, with the literature focussing on (classes of) subadditive valuation functions, and various polytime, budget-feasible mechanisms, achieving constant-factor approximation, have been devised for the special cases of additive, submodular, and XOS valuations. However, for general subadditive valuations, the best-known approximation factor achievable by a polytime budget-feasible mechanism (given access to demand oracles) was only $O(\log n / \log \log n)$, where $n$ is the number of items. We improve this state-of-the-art significantly by designing a randomized budget-feasible mechanism for subadditive valuations that achieves a substantially-improved approximation factor of $O(\log\log n)$ and runs in polynomial time, given access to demand oracles.

cs.GT↗
arXiv2026

Online Algorithm for Fractional Matchings with Edge Arrivals in Graphs of Maximum Degree Three

We study online algorithms for maximum cardinality matchings with edge arrivals in graphs of low degree. Buchbinder, Segev, and Tkach showed that no online algorithm for maximum cardinality fractional matchings can achieve a competitive ratio larger than $4/(9-\sqrt 5)\approx 0.5914$ even for graphs of maximum degree three. The negative result of Buchbinder et al. holds even when the graph is bipartite and edges are revealed according to vertex arrivals, i.e. once a vertex arrives, all edges are revealed that include the newly arrived vertex and one of the previously arrived vertices. In this work, we complement the negative result of Buchbinder et al. by providing an online algorithm for maximum cardinality fractional matchings with a competitive ratio at least $4/(9-\sqrt 5)\approx 0.5914$ for graphs of maximum degree three. We also demonstrate that no online algorithm for maximum cardinality integral matchings can have the competitive guarantee $0.5807$, establishing a gap between integral and fractional matchings for graphs of maximum degree three. Note that the work of Buchbinder et al. shows that for graphs of maximum degree two, there is no such gap between fractional and integral matchings, because for both of them the best achievable competitive ratio is $2/3$. Also, our results demonstrate that for graphs of maximum degree three best possible competitive ratios for fractional matchings are the same in the vertex arrival and in the edge arrival models.

cs.DS↗
arXiv2026

Sequential Linear Contracts on Matroids

In this work, we study sequential contracts under matroid constraints. In the sequential setting, an agent can take actions one by one. After each action, the agent observes the stochastic value of the action and then decides which action to take next, if any. At the end, the agent decides what subset of taken actions to use for the principal's reward; and the principal receives the total value of this subset as a reward. Taking each action induces a certain cost for the agent. Thus, to motivate the agent to take actions the principal is expected to offer an appropriate contract. A contract describes the payment from the principal to the agent as a function of the principal's reward obtained through the agent's actions. In this work, we concentrate on studying linear contracts, i.e.\ the contracts where the principal transfers a fraction of their total reward to the agent. We assume that the total principal's reward is calculated based on a subset of actions that forms an independent set in a given matroid. We establish a relationship between the problem of finding an optimal linear contract (or computing the corresponding principal's utility) and the so called matroid (un)reliability problem. Generally, the above problems turn out to be equivalent subject to adding parallel copies of elements to the given matroid.

cs.GT↗
arXiv2025

Normalizations of factorizations over convex cones and their effects on extension complexity

Factorizations over cones and their duals play central roles for many areas of mathematics and computer science. One of the reasons behind this is the ability to find a representation for various objects using a well-structured family of cones, where the representation is captured by the factorizations over these cones. Several major questions about factorizations over cones remain open even for such well-structured families of cones as non-negative orthants and positive semidefinite cones. Having said that, we possess a far better understanding of factorizations over non-negative orthants and positive semidefinite cones than over other families of cones. One of the key properties that led to this better understanding is the ability to normalize factorizations, i.e., to guarantee that the norms of the vectors involved in the factorizations are bounded in terms of an input and in terms of a constant dependent on the given cone. Our work aims at understanding which cones guarantee that factorizations over them can be normalized, and how this effects extension complexity of polytopes over such cones.

math.OC↗
arXiv2024

Linear Contracts for Supermodular Functions Based on Graphs

We study linear contracts for combinatorial problems in multi-agent settings. In this problem, a principal designs a linear contract with several agents, each of whom can decide to take a costly action or not. The principal observes only the outcome of the agents' collective actions, not the actions themselves, and obtains a reward from this outcome. Agents that take an action incur a cost, and so naturally agents require a fraction of the principal's reward as an incentive for taking their action. The principal needs to decide what fraction of their reward to give to each agent so that the principal's expected utility is maximized. Our focus is on the case when the agents are vertices in a graph and the principal's reward corresponds to the number of edges between agents who take their costly action. This case represents the natural scenario when an action of each agent complements actions of other agents though collaborations. Recently, Deo-Campo Vuong et.al. showed that for this problem it is impossible to provide any finite multiplicative approximation or additive FPTAS unless $\mathcal{P} = \mathcal{NP}$. On a positive note, the authors provided an additive PTAS for the case when all agents have the same cost. They asked whether an additive PTAS can be obtained for the general case, i.e when agents potentially have different costs. We answer this open question in positive.

cs.GT↗
arXiv2024

Non-Adaptive Prophet Inequalities for Minor-Closed Classes of Matroids

We consider the matroid prophet inequality problem. This problem has been extensively studied in the case of adaptive mechanisms. In particular, there is a tight $2$-competitive mechanism for all matroids. However, it is not known what classes of matroids admit non-adaptive mechanisms with constant guarantee. Recently, it was shown that there are constant-competitive non-adaptive mechanisms for graphic matroids. In this work, we show that various known classes of matroids admit constant-competitive non-adaptive mechanisms.

cs.GT↗
arXiv2024

Matroid Bayesian Online Selection

We study a class of Bayesian online selection problems with matroid constraints. Consider a vendor who has several items to sell, with the set of sold items being subject to some structural constraints, e.g., the set of sold items should be independent with respect to some matroid. Each item has an offer value drawn independently from a known distribution. Given distribution information for each item, the vendor wishes to maximize their expected revenue by carefully choosing which offers to accept as they arrive. Such problems have been studied extensively when the vendor's revenue is compared with the offline optimum, referred to as the "prophet". In this setting, a tight 2-competitive algorithm is known when the vendor is limited to selling independent sets from a matroid [Kleinberg and Weinberg, 2012]. We turn our attention to the online optimum, or "philosopher", and ask how well the vendor can do with polynomial-time computation, compared to a vendor with unlimited computation but with the same limited distribution information about offers. We show that when the underlying constraints are laminar and the arrival of buyers follows a natural "left-to-right" order, there is a Polynomial-Time Approximation Scheme for maximizing the vendor's revenue. We also show that such a result is impossible for the related case when the underlying constraints correspond to a graphic matroid. In particular, it is $\texttt{PSPACE}$-hard to approximate the philosopher's expected revenue to some fixed constant $α< 1$; moreover, this cannot be alleviated by requirements on the arrival order in the case of graphic matroids.

cs.GT↗
arXiv2023

Single Sample Prophet Inequality for Uniform Matroids of Rank 2

We study the prophet inequality when the gambler has an access only to a single sample from each distribution. Rubinstein, Wang and Weinberg showed that an optimal guarantee of 1/2 can be achieved when the underlying matroid has rank 1, i.e. in the case of a single choice. We show that this guarantee can be achieved also in the case of a uniform matroid of rank 2 by a deterministic mechanism, and we show that this is best possible among deterministic mechanisms. We also conjecture that a straightforward generalization of our policy achieves the guarantee of 1/2 for all uniform matroids.

cs.GT↗
arXiv2022

A Two-Step Approach to Optimal Dynamic Pricing in Multi-Demand Combinatorial Markets

Online markets are a part of everyday life, and their rules are governed by algorithms. Assuming participants are inherently self-interested, well designed rules can help to increase social welfare. Many algorithms for online markets are based on prices: the seller is responsible for posting prices while buyers make purchases which are most profitable given the posted prices. To make adjustments to the market the seller is allowed to update prices at certain timepoints. Posted prices are an intuitive way to design a market. Despite the fact that each buyer acts selfishly, the seller's goal is often assumed to be that of social welfare maximization. Berger, Eden and Feldman recently considered the case of a market with only three buyers where each buyer has a fixed number of goods to buy and the profit of a bought bundle of items is the sum of profits of the items in the bundle. For such markets, Berger et. al. showed that the seller can maximize social welfare by dynamically updating posted prices before arrival of each buyer. Bérczi, Bérczi-Kovács and Szögi showed that the social welfare can be maximized also when each buyer is ready to buy at most two items. We study the power of posted prices with dynamical updates in more general cases. First, we show that the result of Berger et. al. can be generalized from three to four buyers. Then we show that the result of Bérczi, Bérczi-Kovács and Szögi can be generalized to the case when each buyer is ready to buy up to three items. We also show that a dynamic pricing is possible whenever there are at most two allocations maximizing social welfare.

cs.GT↗
arXiv2020

Approximating Stable Matchings with Ties of Bounded Size

Finding a stable matching is one of the central problems in algorithmic game theory. If participants are allowed to have ties and incomplete preferences, computing a stable matching of maximum cardinality is known to be NP-hard. In this paper we present a $(3L-2)/(2L-1)$-approximation algorithm for the stable matching problem with ties of size at most $L$ and incomplete lists. Our result matches the known lower bound on the integrality gap for the associated LP formulation.

cs.GT↗
arXiv2019

The Aggregation Closure is Polyhedral for Packing and Covering Integer Programs

Recently, Bodur, Del Pia, Dey, Molinaro and Pokutta introduced the concept of aggregation cuts for packing and covering integer programs. The aggregation closure is the intersection of all aggregation cuts. Bodur et. al. studied the strength of this closure, but left open the question of whether the aggregation closure is polyhedral. In this paper, we answer this question in the positive, i.e. we show that the aggregation closure is polyhedral. Finally, we demonstrate that a generalization, the k-aggregation closure, is also polyhedral for all k.

math.OC↗
arXiv2019

On the approximability of the stable matching problem with ties of size two

The stable matching problem is one of the central problems of algorithmic game theory. If participants are allowed to have ties, the problem of finding a stable matching of maximum cardinality is an NP-hard problem, even when the ties are of size two. Moreover, in this setting it is UGC-hard to provide an approximation for the maximum cardinality stable matching problem with a constant factor smaller than 4/3. In this paper, we give a tight analysis of an approximation algorithm given by Huang and Kavitha for the maximum cardinality stable matching problem with ties of size two, demonstrating an improved 4/3-approximation factor.

cs.GT↗
arXiv2018

Simple Games versus Weighted Voting Games: Bounding the Critical Threshold Value

A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of~$2^N$ into a set~$\mathcal{L}$ of losing coalitions~$L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$ with $v(W)=1$. Simple games with $α= \min_{p\geq 0}\max_{W\in {\cal W}, L\in {\cal L}} \frac{p(L)}{p(W)}<1$ are exactly the weighted voting games. We show that $α\leq \frac{1}{4}n$ for every simple game $(N,v)$, confirming the conjecture of Freixas and Kurz (IJGT, 2014). For complete simple games, Freixas and Kurz conjectured that $α=O(\sqrt{n})$. We prove this conjecture up to a $\ln n$ factor. We also prove that for graphic simple games, that is, simple games in which every minimal winning coalition has size~2, computing $α$ is \NP-hard, but polynomial-time solvable if the underlying graph is bipartite. Moreover, we show that for every graphic simple game, deciding if $α 0$.

cs.GT↗